That's much more common, cool, all right. So I'm going to go ahead and get started and you have all heard all of my pre-ramblin here but this is the Lord of the Rings and information security in your open source project. I am Amy at Amy on Twitter and I'm also Amy at Red Hat. I am more than willing to be stopped and heckled and questions and all of that as we go through this. This is about a 20 minute rant or so and then I'm again happy to take questions. So do not feel shy. So from time to time in your information communities, you are going to be able to have things happen to you.  Well that leads you open towards problems later on if you haven't actually written them down and it turns out that the story of the Lord of the Rings is a great method to be able to follow towards actually fixing these things when they happen to you. Out of curiosity, how many people have actually had something like this happen to them? Only one, only two? Okay, so okay.  The rest of you just don't know yet. This will come for you, it will be great. So for me, this came from working at a hosting company when Heartbleed came out. And yeah, oh yeah. So it was one of those things where the release had come through on Twitter for Heartbleed and I kept seeing it come through and I had this reaction of, huh, that's kind of interesting. I now realize that when I have that reaction of, huh, that's interesting, I very, very quickly want to get to the sense of gigantic impending doom or everything is fine. I want to spend the least amount of time in the, huh, that's interesting. What happened for us was we ended up, seeing this come through all the way around the world and one of my Australians who I happened to be working with and I was based out of West Coast, he's based out of Sydney, jumps into chat and is like, hey you guys, we've got a thing. We've got a thing. And it turned into kind of like a lighting of the beacon sort of thing across the world in terms of like, pagers went off and like, you know, people got woken up out of bed and it was kind of like, huh, this is going to be going on for a little while. You know, we should call for aid. And that's the lighting of the beacons and this is where like my concept of the Lord of the Rings came from. So again, it may be cheesy, but it's fun. So I tell you that story to let you know where I started from. And now where I am is a, I am the Gloucester community lead at Red Hat and my focus to be able to feed and water and move that community forward. I can't do that if I don't have good solid infrastructure and I can't do that. And frankly, all of our projects cannot move forward if we're not paying attention to this. So this is why it matters. Okay, yes, we're all very serious about this. So the forging of the ring. Every time that you bring up that server or someone brings up like, oh, I don't know, PH may admin and kind of forgets about it. Yeah, no one's ever had that happen before. No, right? I mean like, pick any interesting thing, service you are going to need with your project. If it has a material impact towards you being able to ship, you should write it down. And I realize that two factor authentication is deeply annoying, but it may in fact be the best thing that we have. So we should use it and being able to practice, better management of information of SSH keys. Don't share them, don't push them around and things that we think, oh yeah, we'll remember that later, we'll fix it. We'll go back and fix it. Just don't do it in the first place because you have the power to forge the ring. And then there becomes a cast of characters. I actually don't think that there's a Sauron in this because no one deliberately does this. You would never deliberately set this up for yourselves. But you can turn into Gollum. If you're the one that finds it and then kind of forgets about it and wanders off and like later on you go, oh man, why is that server there? Why are we doing that with that again? Huh, you've been poisoned. You've turned into Gollum. Frodo is the poor hapless discoverer that ends up actually looking at the logs and going, huh, that's interesting. Huh, what do we have in there? Gandalf is the senior staffer who can read the logs and go, man, you got a thing in there. Right, he throws it into the fire, he reads the logs and you go, oh God, what do you have in there? But the problem is Gandalf doesn't actually come with you on discovery. Gandalf kind of rides off somewhere else and gets pulled off to another bug and he comes in periodically and checks in on you like, so, how are things in there? Oh, huh, you got a thing in there. All right, cool, let me know how you go. And they come back in. There may also be an array of Gandalfs, you may have multiple Gandalfs that come into your management of any incident. The hobbits are the other people on your team who are going to be able to help and each one of them has a piece of knowledge to be able to bring to the table. So, the fun stuff comes in where sometimes you will have Strider and Strider is information security. They come in as you're on your way towards Rivendell, you know that you have a problem, you're now walking towards being able to get through what actual remediation would look like where we're going to go here and information security comes in and says, ooh, I think we can help. We think we know what we're doing here. Everybody hobbits on the way, let's do this. They're probably way less excited about that. I don't think I've ever heard it in information security. I'd be really, really excited about things or a girl in that way. So, you're at the point where you have realized that the impending doom is on you. You rapidly need to fix something. This is your journey to Rivendell. Oh, come on, pick up. Well, next slide should be about communication and why it's not actually moving. I'm not really sure, but it doesn't want to communicate, apparently, if I go back and then forward. There it is, cool. So, communication, we should do that. This is kind of what got us into the first mess, typically. I mean, very rarely you will run into something that has a level of heart bleed. It's usually going to be something much smaller. So, you communicate with the team around you. You communicate with the management structure of not only the project that you're working with, but other people who will need to know. I am hoping that you will have information security alongside you when this happens to you, not if, but when. You will also need legal, because there actually are people that are going to care about this, even if you're just an open source project. People should be using your project, and hopefully, if you're doing it right, they're using it for critical things, because you're important, right? Public relations is going to be important longer down the road, because you will want to be able to say, no, no, cool, we destroyed it, the ring is done, all is well, this is how we've cleaned up the shire. Things are great. Previously, when I've been in these before, I have done things like keeping a running document of what is going on where, who is responsible for what, what are we doing, how is this moving along? Also keeping asynchronous private communication on unlisted IRC channels was another way that I have done this in the past. I don't know if I will do this in the future. This worked for me as this happens to me. I've also done daily calls to be able to confirm current status, next steps, where are we going? Again, your mileage may vary. This keeps the pace moving so that everyone knows where we are going. And what does done look like and what does success look like informs how your weeks move. Sometimes you may end up in a situation where finally fixing the incident is going to take things well outside of your hands and it may take months. May this never happen to you, but it does. And so understanding here are things that we need to work with longer term, short term, and moving on from there. Questions, comments, stories? I know, I realize I'm actually giving like the real part of the talk instead, just Lord of the Rings, we'll get back to that, it's fine. And the actual remediation lines up to make a checklist, follow that checklist, remember that having that checklist is going to be able to save you from other problems down the road. So the way this works is, okay, you've made it to Rivendell, you have the Council of Elvron, everyone who needs to be involved is there, hopefully. You know, you'll have the elves, sometimes they're helpful, sometimes they're not, you can't really be sure, but they're definitely there, they're going to be there. You'll find out later, the dwarves want to get this done as soon as possible and infosec may also be involved, sometimes they're men, sometimes they're dwarves, sometimes they're elves, chews. Other pieces around in here, the minds of Moria end up when you didn't quite get through discovery or something got missed in discovery. Something that should have been remembered was not. And then you end up in this kind of terrible place of either something leaked, something worse happened. You were not sure what to do next, so it became a lot more urgent. Maybe the minds of Moria never happened to you, but now you can use this. When something happens, you're like, oh, we should have remembered that. We're in the minds of Moria, everyone. And a note on legal, because sometimes legal will come down as gladrile. They want to help you. They want to be able to move all of this forward. They want to be able to make sure that all of this is going to come out and the best light possible for you. And I actually probably need to give another version for the legal side of this, so that's another talk. But sometimes legal can be Boromir. And sometimes Boromir is like, no, no, no, no, I'm taking this and it's never going out.  And this will probably never get out in public and this will probably never be something you talk about ever again. Honestly, there's not much to do about Boromir. The better way is not to have any information security problems in the first place, but we'd like another world. What will certainly happen next at this point is you will get halfway through where you say done is and half your team is going to get pulled off to work on another bug. Also, all the hobbits getting kidnapped. So the Eye of Mordor is the press. Sorry, the Eye of Sauron ends up being the press because you do not want them to be able to find out about this until you have destroyed the ring and everything is beautiful. And you have gotten to the point where, no, we understand there was a problem, we have resolved it. This is the things that we did to be able to resolve it. We're done, or here's how everyone knows about it and this is what everyone is going to do moving forward. And your ultimate goal is by things, don't actually work, come on, Slides, there. That is what success looks like. Success looks like we are better than before. We know much more about our infrastructure. We have all of this knowledge. We know pieces that we didn't know before and we are the better for it. This is what success looks like back in the Shire. On the other hand, you may also realize that you may turn into the hobbit again the next day, depending on just the way that the internet works. And the fact that all of our systems are so much more complex than they were four years ago. The things that we are working on now are the things that Google was thinking about in production and now they're all of our problems. It's just, no, it's true. It's like all of the things we're like, oh, God, yeah, four years ago. Wow, that's a really interesting idea. Now, this is currently my problem. Awesome. I really hope I've written that down. So congratulations. You've survived the shadow of the game show of Infosec on your doorstep. So my real advice is making sure that you actually are communicating within your team as you find out about it. Being able to solve that question of, that's interesting, that's really interesting. You want to know as soon as possible, hopefully within hours of having that feeling. You may not always be able to do that. Work as you get towards the end of this, towards running a really good root cause analysis, which ostensibly will help you prevent or change things about the way that your community's process is working for when this happens again, or being able to communicate with other communities that this happens with because you may possibly have cross-pollination with some of their work. Do make sure that you actually have the right people involved as well. At least in those beginning meetings and in the root cause analysis meetings, and those tend to be really epic meetings if you run them right, that's another chalk entirely. So I won't go into that too much, but also making sure that you do have the information within your own circle of trust. Everyone that is on the quest should actually know that they are on the quest. You would be surprised how people don't actually know that, no, no, no, some of this stuff should not actually, don't put that on Twitter, don't. And the words of David Foster Wallace, I wish you way more than luck. So, thank you. Other stories, comments, questions, things that people want to be able to talk about. Yeah, nothing? You have no war stories. Yes, it's more about knowing what you're, feeling like you know how to be able to handle them when they do happen. Because trying to prevent them is like trying to prevent water running downhill and like also Chinese hackers. Oh wow, okay, great. Shooting the messenger. Yeah, because it's your story, I won't retell it for the recording, but the, I attempted not to be able to have like the, here's how serious these things can be because that's a huge downer. I mean, I feel like the ring of power that could destroy us all is probably enough, you know. But like these things matter and there's a reason why you have to take them very seriously when they do. So, thank you.


It depends on whether or not students started their undergraduate degrees directly after high school or secondary school, in which case they may be 21, 22, 23 years old when they begin their graduate study. But I think one of the things that again distinguishes graduate education and nowadays even undergraduate education is the range and ages in which people pursue education. There's great variety. And again, that's one of the fantastic things about the U.S. education system. You can start off at in your 20s, go and work for a while, come back in your 60s or even 70s.


Right, so today we will go on with our study of phase transitions and we will have a general introduction to what is called the Landau theory. Now I am not going to do this, we do not have time to do this in great detail or at any length but what we are going to do is to take off from a familiar model namely the Ising model which we have all been looked at and then I will simply make a statement that a very large class of phase transitions will fall under the so called Ising universality class. So whatever happens here is generic to whatever happens in general and I will use the same symbols that we use for the Ising problem. In other words the order parameter is a magnetization, I use a little m for that, we will continue to do that but the physical significance of this m could change from problem to problem and you will see that the structure of the theory is more or less generic, it is quite general and then we will go on to some introduced fluctuations and go on to what is called the Ginsburg-Landau theory and hopefully finally we will talk about dynamic critical phenomena. So we take this in several steps, let us start with some familiar material and it is as follows. I will draw a number of pictures today to show you what the phase transitions, what various diagrams, phase diagrams look like. So wherever the algebra gets a little unnecessarily complicated we will simply draw a picture and go ahead with things and there will be a lot of hand waving arguments which can be made rigorous but I want to communicate the essential physics of what we are talking about. So we start again with the Ising model for which if you recall we had an equation of state. So we had an equation of state for the Ising model and we are dealing now with the critical region, we are looking at the region near the critical point. If you recall the critical point is characterized by a temperature Tc, the Curie temperature at which the system goes from paramagnetic to ferromagnetic. The critical value of the field which is equal to 0 in this case because it is a 0 field that you cross over from paramagnet to a ferromagnet, spontaneous magnetization is in the absence of the field and of course the critical value of the magnetization is also 0 because it takes off from 0. Now just to recall to you what the diagrams were in this case, I plot an h versus m then the critical isotherm did this, critical isotherm. So it c was 0, m sub c was 0 and then we also had a figure, let me draw this again, just to recall to you we had m versus t and here is Tc in this case and the magnetization in the absence of a field m not was 0 beyond t above Tc and then it went down like this or the ferro down was a branch like this and this branch became unstable. So this was m not, this spontaneous magnetization and again by critical region I mean this region, just as I mean this region, critical region and finally there was the h versus t graph and the h versus t graph was a line like this and then at Tc. So again this is the critical region, so hc was 0 and Tc is at this point here. So it is this circle region that we are dealing with, we are talking about and what happened in this circle region was that in the Ising model in main field theory we ended up getting an equation of state and that equation of state read like this, we had tan hyperbolic h over kT but essentially in the critical region h is near 0, so it was h over kT was equal to m minus tan hyperbolic mTc over T divided by 1 minus m tan hyperbolic mTc over T. Now we are going to focus on the critical region namely T near the critical temperature, so let us introduce the reduced temperature T equal to T minus Tc over Tc. Then I can write this equation here in terms of critical quantities very close to the critical region in terms of little t and little m, m minus mc is the same as m because mc is 0, h minus hc is again just h because hc is 0. So this equation can be written in the form on this side mT that is the leading term and then the next term is of order m cube and then plus order Tm cubed, so we will drop this it is a higher order term. Spontaneous magnetization is found by putting h equal to 0 in this and then the equation is m cube plus mT is equal to 0, so you have m cubed is minus mT, m equal to 0 is always a root but for T less than Tc that is unstable and for T negative namely T less than Tc out here this region, m squared is equal to T mod T was the solution and therefore you got plus or minus square root of little t out here, so that was the mechanism. Now we want to make this systematic and one way to do this is to argue and this is Landau's argument it proceeds in a large number of steps, so let me say what it was start with one way to look at it is to say there is probably there is it is possible to introduce a potential after all this equation of state has essentially a reason by saying some thermodynamic potential is at a minimum so that you are in thermal equilibrium. In this case essentially the equivalent of the Gibbs free energy because we have an h here the analog of the pressure and we have the analog of the volume out here and the temperature that is the equation of state, so at a given value of the magnetic field h 0 or otherwise it is equivalent to saying at a given value of the pressure and temperature so equal to the Gibbs free energy. We are not going to write that down let us go back and do a bit of phenomenology and say essentially this is the equation that I have so I understand from this equation how you get this square root here the same equation gave us this cubic here the same equation gave us the susceptibility also remember that we plotted the susceptibility as a function of t I plotted the isothermal susceptibility and it diverged at the point tc like 1 over little t all these things came out of this equation of state here. So let us do the following let us introduce some potential on differentiating that potential with respect to m and setting the result equal to 0 I get this equation of state you could call it the Landau functional or something like that. So this potential it is not exactly the Gibbs free energy it is not exactly the Hemolds free energy because those things have to satisfy certain convexity properties these potentials do not this is just an empirical this is an equation of state at the critical region. So let us define a phi which is a function of m t and h equal to some constant phi naught which is a function of t and h does not involve m and I want to produce this equation of state so minus m h. Let me just for convenience you could write this t as tc plus a small correction the correction is a higher order correction so it is essentially tc here and we can subsume it in h so it is not an essential factor here I have already done that see you see I have already got a tc here this is essentially tc because if I multiply through it is going to the correction t minus tc is going to give me higher order terms no it will be of order t squared it will be of order t squared because if I write this as tc plus little t essentially and I take that little t across there it goes away only the tc part contributes the next term is of order little t squared which I have neglected yeah you need that yes okay you have okay good question you have to check and I am not going to do this here you have to check that is consistent to subsume this t here and call it just tc yes good exercise check that like I have neglected this term for instance okay exactly exactly yeah exactly so this is the consistent this term is not relevant I call it h okay so if you do this minus mh plus t m squared it is this this term here plus m4 and then you compute delta phi over delta m and you set it equal to 0 you get precisely this put a 2 here put a 4 here if you like these are constants which I am not paying attention to so do you agree that if I take this phi and I differentiate with respect to m and set it equal to 0 if you like yeah if I set delta phi over delta m equal to 0 I get this equation so my claim is that this potential whatever it is this phi has a certain geometric shape and its minimum will give me the equilibrium state we can plot that we can plot that fellow in order I am going to generalize that this is the original random functional because the point is eventually what I am going to argue is that the factors here the signs are very important there could be numerical factors which I have not bothered about so I am going to have a term which is proportional to the product of the order parameter and the field then a term proportional to the square of the order parameter with a little t in the coefficient as a leading coefficient and then a term which is essentially a constant coefficient times the 4th power of the order parameter that will generically give me this second or this continuous phase transition and it will generate for me all these magnets so that is the idea and then I am going to argue that these coefficients could in general be temperature dependent but we have looked at the leading temperature dependence near the critical point okay. So let us draw some pictures and see what happens notice also that you could do the same thing with fixed field suppose you plotted the magnetization versus t for small positive field then the curve would be this is the paramagnetic region and then this would be the furrow region eventually it would saturate similarly on the negative side a small negative field if you do not switch it off will behave in this fashion so what you are doing is drawing these isotherms for non-zero value these various isotherms and looking at what happens as you change keep h fixed and you decrease the temperature from above tc to below tc so as you go up here or as you go down here in the case of the magnetization versus temperature it means if you keep the field fixed at some positive value you are here at this point and as you change the temperature you come down for a fixed value of the field you are going to jump this make a transition here as you change the field from positive to negative values keeping the temperature constant you are going to jump here that is equivalent to saying if I go from here to here keeping the temperature constant I cut across this phase transition line that is like the liquid gas coexistence line and there is a discontinuous change in the magnetization from this point to this point so this is a line of discontinuous transitions ending in the critical point where the transition becomes continuous in other words the discontinuity in the magnetization keeps decreasing till it vanishes at the critical point which is why it is called a continuous transition okay well that is going to be encapsulated in the figures that we can draw we can now draw ask what is what is this potential look like in these cases so let us draw these potential this potential so let us draw let us have t greater than tc t equal to tc and then t less than tc let us draw these 3 cases separately and let us draw them for h equal to 0 0 feet so this fellow is gone and I am going to draw phi minus phi naught so this is just a constant as far as m is concerned I move it aside and plot this graph here so I have tm squared plus m4 and that is now easy to see what is going to happen for t greater than tc so I plot phi minus phi naught always and what does the potential look like as a function of m always the order parameter m then at h equal to 0 this is gone t greater than tc this is positive this coefficient starts with a parabolic behavior and then takes off like a fourth power so the minimum is a simple minimum it is not quite a parabola but it is like this 40 greater than tc at t equal to tc the same thing as a function of n little t is 0 now and the field is 0 so you have a pure quartic term therefore this looks like a very flat and t less than tc you have an inverted parabola the field is 0 and then you have the m4 which takes you up so let me plot with a cross or dot the equilibrium value which is the state of thermal equilibrium and give you the order parameter at thermal equilibrium it is obviously 0 here it is still 0 here but now it is either this or that these are the two values of the spontaneous magnetization that you saw in the m versus t m naught versus t graph either up or down up or down this is for h equal to 0 so let us plot the same things take this up a bit t greater than tc t equal to tc t less than tc let us plot the same thing for h small positive on this side now h is positive this fellow is positive so near the origin you have a linear behavior with a negative slope so this curve for t greater than tc looks like something like this because near the origin you have this thing then you can find the minimum by working that out by taking its minimum there t equal to tc what happens at t equal to tc in this case but h is positive t equal to tc this fellow goes away and you still have a curve which looks like this it changes shape here a little bit so this guy gets a little flatter and then he does this and for t less than tc what does it do it will still be like that but it will be it will bias it towards this so near the origin if h is less than 0 there is a linear term so essentially there is a thing like this and there is something like that bias towards the positive side so the absolute minimum is still here on the positive side on the other hand for h less than 0 for h less than 0 for t greater than tc you have a positive slope here and t greater than tc that fellow is still a square and so on it will be simply a reflection something like that that is the equal thing and it will do the same thing you come down and then broaden out and let me do this again it is on the negative side but now for h less than 0 and t smaller than tc we will have this slope but we will have a deeper deeper minimum and we will have a negative thing so at t equal to tc we have seen what happened already positive slope I mean h positive you have a minimum at a positive value h negative you have a minimum at a negative value at tc you have this at 0 right so this corresponds to what do these 3 graphs correspond to they correspond in this h versus m graph on the critical isotherm you are describing this point this point and this point that is the critical isotherm so on this thing case you are describing this point here corresponds to this minimum this value it passes through corresponds to this flat minimum and this value here corresponds to this minimum on the other hand when you go to t less than tc here you are going through a first order phase transition because now you are looking at this here is t here is tc and you had the spontaneous magnetization curve like this and then you had the other curves in the presence of small positive and negative fields like this but now t is less than tc so you are to the left of this curve you are going like this as you are going from positive to negative values of the field so you are really crossing this is m if you do this in the t versus h graph you had this graph with tc you are crossing this line you are going through a first order phase transition from a positive magnetization to a negative magnetization so the way the free energy graph or the energy function or the landoff functional changes shape is first you have a graph with two minima but this is the global minimum and therefore the equilibrium state is a positive value of magnetization at the critical value at tc the two minima are equal and below for negative fields the left hand side minimum becomes more pronounced in the top so this is exchange of stability that has happened in some sense so from this minimum you went to case were equally probable and then this became lower so you went from here to here discontinuously crossing this line here so you can see that this generic form already encapsulates in it all that is happening here both the first order transition below the critical point as well as the critical region itself within main field in the simplest of approximations so the way to generalize this is now deep very deep this is such a generic thing that one starts by saying that now let us look at this picture in general we still not introduced any fluctuations remember that the crucial point the assumption was that we had a term in the Hamiltonian which look like ij jij si sj so the Hamiltonian was this minus h time summation over i si and I wrote this as equal to minus summation hi si over i where hi was equal to summation j equal to nearest neighbor of i jij expectation sj out here plus h applied field so essentially I replace the expectation of this term by si by this term by si times expectation sj in other words I neglected the fluctuation in sj so essentially I wrote sj equal to sj plus sj minus sj and neglected this in mean field that is really what has happened I neglected the fluctuations so we have still we have not gone we have not taken that into account really so we are within mean field theory this in this model mean field theory simply means this I think more than that and we got an m which is spatially independent of where you are in the lattice it is completely homogenous etc etc we will subsequently put in spatial dependence a little bit later because we want to include fluctuations in some sense but the original Landau theory itself starts by saying that for a given problem with an order parameter I introduce a functional phi which as a power series in the order parameter is something like summation n equal to 0 to infinity in principle some coefficients C n which are functions of the set of all the exchange constants the field and all the other parameters so it is functions of all these quantities multiplied by temperature etc multiplied by m to the power n this is the order parameter so I construct such a functional out here and now I ask what are the possible values of n so if I were to write this out this would be of the form C naught plus C 1 times m plus C 2 times m square plus C 3 times m cube plus C 4 times m 4 plus dot dot dot now as far as the critical region is concerned we have seen that all that you need is to keep up to the 4th order term in it do not need anything else so we are trying to describe that sort of a scenario here so first step this is replaced by 4 so we do not have to go beyond that second point this is a constant and we can drop it it is not doing anything when I differentiate etc etc so this is a harmless constant but this term here cannot exist because if it existed it would say that there is a solution m not equal to 0 above T c because if I differentiate at this fellow here and end up with the constant term here so in the potential you cannot have a term which is linear in the order parameter look at what happened there because if you did you can easily check for yourself that if you had such a term in the potential if I differentiate delta phi over delta m and put it equal to 0 I get a constant C 1 independent of m which would not go away even above T c so it would end up with a solution for m not equal to 0 above T c which we do not want because we started by defining our phase transition as such that the order parameters 0 above the critical point and non-zero below the critical point so this term goes away these terms exist but now the argument is wait now this is with H not equal to where with for for H set equal to 0 no C 1 if H equal to 0 yeah I should say that if H is not 0 then of course there is a linear term that is very much there that is what is giving you the susceptibility and so on yes we are going to do that in a second the reason I am singling this out is because you want this if H is equal to 0 this is definitely got to be 0 because by the very statement that the order parameters 0 above the critical point then the next point is that in the absence of the field I want to have symmetry between m and minus m you saw all these figures all that happened was m and m minus m got exchanged as you made the first order transition since you want to retain that symmetry this term is 0 because you want this thing to be invariant under m goes to minus m you can cause this in fancier language you can say that the probability of a given configuration is e to the minus beta times phi and phi of m must be equal to phi of minus m otherwise the probabilities will change in the absence of a symmetry breaking field. So then you have this and you have this and now we have seen that these coefficients could be temperature dependent themselves so this term here would be some C 2 2 0 plus C 2 1 t plus C 2 2 t squared etc. Yes we have assumed that it is analytic in the coefficients and all these exchange constants in the field and then the order parameters. I am not saying this is a convergent power series you are going to truncate it is a finite time finite point and 4 in fact etc. So this term has to be 0 because the only way in which you can get this phase transition critical point is for this term to change sign as you cross little t equal to 0 as you cross t c which means the leading term must be 0 and it must start with the term proportional to t as indeed it is the case here it is because this term change sign that you had solutions for m which are not equal to 0 plus or minus square root of minus mod t to the half of mod t to the half you got that because there was a linear term there. So this term is 0 and we retain only this term. Then similarly C 4 will also have a C 4 0 plus C 4 1 times t plus C 4 2 times t squared etc. Now the only role of that 4 power term is that you want stable minima. So when m becomes very large in the positive or negative side you want the well to point up the concave upwards then downwards. So for stability thermodynamic stability you want this to have a positive coefficient. The temperature dependence of it is not very significant. So you may as well retain only this term and throw out all these terms and you end up with precisely this. So now let us write that in kind of fancy notation.  This is the land of and all the information I want comes out of this potential. Now the question is what is the guarantee that this mean field is valid. So when is it valid? We need to know when this is valid. Well let us ask that question separately. Let us ask. We are going to put in all the information that we already have in this business. I have already said that all these critical exponents come from just the correlation function, essentially the behavior of the correlation function. That is the correct way to look at this. So I am going to use that information without actually proving it. We have said certain things about this correlation function. I am going to use that without actually using without actually proving it in some sense. So I would say that it is valid as long as you can neglect fluctuations. Now when can you neglect fluctuations? Because what is really happening is that the system is correlated. You cannot say all the spins are independent within some correlation length xi and we also I mentioned that the xi diverges as you hit the critical point. So if you recall we had a G which I called ri minus rj and I call this SiSj minus SiSj this fellow here. So product of expectations and the non-zero nature of this G probes fluctuations because correlations because if this is completely uncorrelated then this thing would be 0 identically. So good measure of this and we also saw several properties of this. I related this to the susceptibility, static susceptibility and so on. Now a measure of this would be to say that if within a correlation length you compare this quantity to the magnetization itself namely to the factored form below. So divide this by SiSj and compare how big this is compared to this guy. That will give you some idea of how accurate this mean field theory is. So if this ratio is much much less than 1 I would say this is the relative error in this quantity and that is a good measure of the fluctuations. So that would be one way of doing this. Let us sum over this i and j in any case. So finally this whole thing reduces to the following. An integral in d dimension so let me be working d dimensions, spatial dimensions d dr and then this is G of r which is mod Si minus Xj etc. We computed this quantity divided by integral d dr m squared of r. So I have course grained in a volume of size, linear size the correlation length and I am comparing the two. So I got to integrate over a volume, over a volume V where V is of orders right to the power d. We are going to sum over i and j on top and then below and find out what is the relative error in this whole business. So that is how I get this. And the volume of integration is not the whole sample. I do not need to do that. I find out within one correlation length because outside it the correlation is 0 anyway essentially. So I need to compute this quantity. But notice that we computed this quantity and showed that it was essentially the susceptibility. So this thing goes to chi t or susceptibility on top. That is essentially what it is divided by the magnetization could be taken to be constant inside a correlation length and it is this value m whatever this is. And we know that in the critical region it goes like t to the beta. That is the magnetization index. So let us write that out effectively. This is t to the minus gamma mod t. Let us put modulus everywhere mod t to the minus gamma divided by this factor is t to the 2 beta because the magnetization exponent was beta the square root of half in mean field theory and this gives me t to the 2 beta. And then a volume d dimensions of linear size xi. So this is xi to the d. So apart from constants of order 1 this thing is mod t to the minus gamma divided by we know that xi itself goes like t to the minus mu. It diverges. So mod t to the 2 beta minus mu d. This must be much much less than 1 as t goes to 0. Then you are safe in neglecting fluctuations. So where does that get us? It says 1 is much much greater than 1 over mod t to the power or rather let us write it like this. Mod t to the power 2 beta plus gamma minus mod t to the 2 beta plus gamma minus mu d must be much much greater than 1 as t tends to 0. That means this exponent must be negative mu d or d greater than 2 beta plus gamma over mu. So only if the spatial dimensionality is high enough is this correct. This must be high enough in any given problem. If it is equal to or less then fluctuations are very important and the smaller it is the fluctuations get more and more important. This quantity this it is called the upper critical dimensionality. Not yet. Yes. So it says that in any of these critical phenomena whenever you have a critical point then depending on what kind of universality class you have there exists an upper critical dimension above which you may as well work in mean field theory because the fluctuations are relatively unimportant and vanish in the thermodynamic limit. They do not affect the exponents or anything like that. Now let us check what it is for the Ising problem because we have an answer in mean field theory. In mean field theory in our problem we had beta equal to half, gamma equal to 1 because magnetization went like plus or minus square root of T C minus T in the critical region. The susceptibility went like 1 over T minus T C. This is the wise Curie-Weiss law. So gamma was 1 and mu was equal to a half in this case. So we have 1 plus 1 divided by half which is 4. So that is the reason you find this statement made in standard textbooks in critical phenomena that in D greater than equal, greater than 4 dimensions the fluctuations are unimportant. Obviously we live in 3 and we have 2 dimensional magnets. So it gets more and more significant. The deviation from the mean field exponents will become more and more significant as D becomes further and further away from the upper critical dimensionality. That is however a lower critical dimensionality below which the critical point itself vanishes. I mean you do not have a critical point. You do not have a phase transition at all because the disorder can never be overcome by the interaction. The effect of entropy is too strong. In the Ising model the lower critical dimensionality is 2. So in less than 2 dimensions you do not have a phase transition. In greater than 4 dimensions, spatial dimensions, mean field theory is good enough but the interesting physics lies in 2 and 3. It is very, very non-trivial in 2 and 3. And that seems to be more or less the case always. So somewhere we should see that we can attach our mean field. Right, exactly. So you have to... So the question, the point is when we computed mean field and we found the phase transition, it said that it predicted a phase transition in every dimensionality. It did not say anything at all. I mean it said independent of D. D did not appear at all. So that was wrong. Mean field theory overlooks that. We know the critical exponents are very dependent on the dimensionality whereas the mean field theory completely ignores that altogether. So experimental evidence rules out the possibility that mean field theory is correct for the Ising model. We know that it is wrong. We can compute in 2 dimensions. We can compute. Yeah. Yeah. Yeah. If you do the renormalization group, you will see the thing at 4 and above. At greater than 4, mean field exponents are exact exponents. Oh yeah, yeah, yeah. Exactly. Now it is a question of whether you know what sort of accuracy you want. We have perturbation methods. We have this D minus, 4 minus epsilon expansions and so on. We need to keep the sufficient number of terms to get that reasonable results. So the computation of the critical exponents for D less than upper critical dimensionality is hard. You could ask what happens at the critical dimensionality itself. Typically of all these cases, very typically, there will be logarithmic corrections. So the corrections are not power law corrections but log corrections. Similarly, you could ask what is the critical region? How small should T be? I have said T is going to 0 but how small should it be? That is called the Ginsburg criterion and I will talk about it next time. We will see how small it should be in order for this to happen. By the way, this whole thing is, the whole renormalization group approach to critical phenomena started off with a lot of empirical observations on scaling exponents. Now let me just write those down since we are not going to use them anywhere. I need to write them down so that you have that at the back of your mind. For the Ising model, for the Ising universality class, yes. For other universality classes, all the mean field itself is different. The Ising universality class includes the Van der Waals kind of model because those are identical to this. They are in the same universality class. So they all have to do with an order parameter which is a scalar. If you looked at the Heisenberg ferromagnet, the order parameter is a 3 dimensional vector and then you are finished. It is a different class. If you looked at the XY model, the order parameter is a 2 vector moving in a plane with 2 components and that is different. So I said that it depends on the spatial dimensionality. It depends on the dimensionality of the order parameter, number of components and it depends on the range of the interaction. Basically these are the only things that govern which universality class a given Hamiltonian belongs to. Now what has been found is that in the critical region and this is how it started in the 1960s, the whole theory of scaling, a lot of these functions of several variables were found to be scale invariant in the sense that they were generalized homogeneous functions. They were functions of combinations of the independent variables. And they led to a lot of empirical scaling relations which today we can justify by somewhat more rigorous methods. Let me just write them down so that you have some information. So let me call it scaling laws between critical exponents. First of all, I said that everything is dependent on the correlation function. So we really need to see what the correlation function does so that we can have this quantity g of r basically s i, s j, minus etc, etc. This quantity went like e to the minus r over psi and then I mentioned what it did at the critical point. This was psi to the power d minus r to the power d minus 1 over 2 psi to the power d minus 3 over 2. This is for r much, much greater than psi. And at the critical point, it goes like 1 over r to the d minus 2 plus 8. And remember we defined the critical exponent for this guy. We also found that psi goes like mod t to the minus mu. So two exponents are introduced in the correlation function. One is the way it diverges at the critical point, the critical region. And the second is what happens to the correlation which changes from an exponentially damped function to a pure algebraic function, a power law, inverse power. This eta is called the non-classical exponent because if you did mean field theory, eta is 0. So let me also write down mean field values in this problem, MFT values, mu equal to half, eta equal to 0. Now what the scaling relations tell you are the following. It is a set of 4 relations so that all the exponents are written in terms of eta and mu. So the first is called the Rushbrook equality in this case. Alpha plus 2 beta plus gamma is equal to 2. This is the specific heat exponent. Specific heat goes like 1 over mod t to the power alpha. This is the magnetization of the order parameter exponent. This guy here is the susceptibility exponent. The second relation says 2 minus alpha equal to mu d. This is called hyper scaling for a reason which I will just mention in a second. So if you give me the dimensionality of space and you give of the system that you are working with and nu then I give you alpha, the specific heat exponent. And then beta plus gamma equal to beta delta. Delta is the critical isotherm exponent. And then the next one is gamma equal to nu times 2 minus eta. So with the help of these relations you can express everything in terms of mu and eta. And what do the mean field values do? MFT values. It says nu equal to half, eta equal to 0. It says alpha equal to 0. It is a finite discontinuity. Mean field predicts a finite discontinuity and jump discontinuity in the specific heat. Beta equal to half, gamma equal to 1, delta equal to 3. What happened here? You notice that all these relations are valid with these values. Alpha plus 2 beta plus gamma is 0 plus 1 plus 1 is 2. Beta plus gamma, half plus 1 is 3 halves. This is 3. This is half. This guy is 1. This is 0. This is half. This is 2. But this, this gets violated by these numbers. Notice that this is the only law, only scaling relation which is dependent on the dimensionality. All the others are independent of the dimensionality. But this depends on the dimensionality. Now this mean field values are valid only above the critical dimensions, upper critical dimensionality. So unless you put d equal to upper critical dimensionality, this relation will not be valid with those values, right? And then indeed it is valid because if you put this equal to half and that equal to 4, then and this equal to 0, that is perfectly consistent. Yeah, but the, well it will work, okay. Two statements here. One is that this relation here for it to be valid with mean field values, you have to put the upper critical dimensionality here. The second point is, it is a separate problem to show, separate thing to show that the effect of fluctuations is negligible above the upper critical dimensionality. That is a separate story. So this is not on the same footing as the rest of it. That is what I am trying to point out. So what we need to do is to pay more attention to fluctuations. This means that our original Landau functional where we just took M to be independent of R is not good. To include fluctuations, you have to allow the fact that the order appears in patches of size Xi typically, which gets larger and larger as you approach criticality. So we need to create a functional that will be the Ginsberg Landau functional in which we have to put in the spatial dependence of the order parameter in some coarse grain fashion, not at each lattice site. But when you coarse grain it into blocks of say size equal to the correlation line, then we should be able to get an effective free energy functional or Landau functional which includes spatial variations. And we will see what happens when we do that. Again we use very general principles. We will use the symmetry arguments. We will use the fact that we want a scalar, etc, etc. Yeah, there will be dependence on the correlation length in the indirect kind of way. Yeah, sure. It will certainly appear. So that will be the next step. Before we do time dependence, we will do that. Then the kinetics of this transition is something we have not talked about at all. That will be the last thing we do where critical slowing down will appear. Just as the lengths, the correlation length diverges, the correlation time also diverges. So things slow down at the critical point and it will create its own exponent. We need to get, we need to deal with that as well. Yeah, that will be the time dependence program. And then we have to include fluctuations in it which we will with a random force and we will be back to our larger model. But this time for not a single particle but for the order parameter itself. So the basic ideas are very straightforward, very simple but the implementation and then the renormalization group is something I have not talked about here at all. We do not have time for that but that is a separate story altogether. All right. So let me stop here.


Wel i'n gweithio i'r TV ym Mhyselwyr Everton, wrth gael i chi i'r prwy o Snickers protein ym Yn Gweithfans, yn ystod yn gweithio i'r ddweud yng Nghymru transfer yw ddweud, dwi'n gweithio ddweud o'r ddweud. Yn gweithio i fi, rwy'n gweithio i'r ddweud o'r Gweithfans Andy McGregor. Rwy'n gweithio i chi. Rwy'n gweithio i'r ddweud, rwy'n gweithio i'r ddweud. Rwy'n gweithio i chi, mae'n gweithio i chi. Let's kick it off with Joshua Zaxie, who has named that, has been bouncing around for the best part of three weeks now I think on and off, obviously it's got, it's kind of piqued the interest of Evertonians today because Paul Joyce, who a lot of people put a lot of faith in, has actually referenced it in an article he's done obviously for Britio Romano, another journalist that's been carrying the story for about 10 days now, but has come back with another update today, saying it's a straight fight between Everton and Parmer. Parmer are offering the player game time, Everton are offering a slightly different path for Zaxie, but Zaxie wants to join Everton over Parmer according to the journalists. Before we get into whether or not we think it'll happen or whatever, what is your initial feeling on Zaxie, what do you think of him as a player? So Zaxie, I think obviously Everton fans know him because he came on trial at a torn once a couple of years ago for us didn't he? He was a star when he was a fine old and then Bayern picked him up, obviously Everton tried as well, Bayern picked him up and he's been doing reasonably well for their new teams and for me, you know, watching him as a player, obviously since his name was dropped, watching a fair bit of him, he's got talent, I'll say he's got talent. I think Everton fans need to be careful with his expectation, I think there's certainly talent there, much like Moise Keane, there's a lot of rough edges that need to smooth them off and I think he's capable of scoring goals, he's got lovely technique, I think he can hold the play needs to improve, position needs to improve, tactical now, all the things the players learn as they develop really and I think that's the major issue with him but now he's got decent feet, 1v1 he can beat a player, he scores, he scores. He's got decent amount of goals for Bayern and obviously they create a lot of good shots, but now he's a nice player, I just think you've got to be careful with what the expectation is. Yeah I've watched a bit of him as well, I've done a little bit of research on him as well and he has got a good touch, you know, lovely little round of corner passes that he produces at times but you're right, his hold up play needs to be tighter but what I would say is physically, you know, 6 for 4 so you know he's got the physical attributes of it, he's not slow. You know, good turn of pace about him but yeah, you're right, there's obviously a lot of refining that would need to be done with him and he wouldn't be someone who would come in and the manager would have a flip of a coin, whether it's him or Dominic Alderley when it's not that kind of striker. It's maybe what Moise Keane should have been, but because of the money we paid for Moise Keane he was never viewed like that obviously he'd played a few games, well he'd done wealthy events, he's scored some goals and we paid a big fee 4 and 25 million whatever it was, 27 million. And that immediately creating expectation doesn't it, this is our main striker and so when he should have been given time to develop, you know, we wanted the same because of the outlay. Joshua Zakesy would be different to that because obviously the rumours of the transfer are alone with, I've seen two, one's alone and then review at the end of the season and the other one is alone with an obligation to buy. So it would give Everton, I guess, the opportunity to look at him, but without the pressure. Is that how you see it compared to the Moise, do you think it's the same kind of thing with Moise Keane but there'd be less kind of pressure on Zakesy? Yeah, I think from Everton's perspective I think we saw the Moise Keane transfer like that, I think Meena Rellwer obviously thought that Moise being a youth star at Juventus and obviously getting some good games at Juventus. I think he thought that he'd be coming in straight into the face here and obviously build himself up for his eventual move. It never happened that way, of course.  You can all have a look at him and see if he's got some potential because if he has got the potential it's unbelievable to have, then 10 million would be a snip really, you know, in the long term. It creates an asset for Everton and he could potentially flip if he does well. As I say, it is more of a trial, you know, sort of thing. I think you'll probably make the bench, don't be wrong, because if you do get rid of a chin-touch or someone, then we'll need that extra striker on the bench, but as I say, it's not someone who's going to come in and impact games off the bench. It's a completely different type of deal and that type of deal it is, but yeah, I think in terms of Zakesy, I think it's a good opportunity for me to pick up a talented player at a lower price maybe. It just depends on how it works out. There's some basic information going to go up on the screen now about Zakesy. So there you go, he's 19 years of age, 6 for 4, like we've said, he's a forward and he's played 16 times and scored 4 goals for Bayern Munich in the first team and now obviously he's played in Bundesliga 2 and he's played in the U team, scored goals at that level as well. But like you said, he's a talented player, but you're right, he is more of someone who we would have to work on. I think obviously if he did come in and touch someone out, he would be the back-up striker, I guess, to Dominic Alvedlun, if that's how you want to look at it, and certainly his physicality would mean that the manager would probably have him on the bench, definitely, you know, and to bring him on in certain games or whatever. But it is one of those that I guess Everton should be picking up if he can, because it does represent the opportunity, even if it is just literally to double your money on him in a year or whatever, you know, smooth down his edges and make money back on him. The flip side to that is if he does really well, you've got, like you said, you've got a bargain on your hands and the quoting, 10 million euros, which is about 8 million quid. So, you know, that would represent a decent bit of business, wouldn't it? Yeah, you don't have to talk about this before. You don't want to buy a special striker to be a back-up, because let's be honest, you never need to be careful on how to allocate the wages, because you want your best players in the best money rather than 100 grand sitting on the bench playing every five or six games, because Dominic Alvedlun is doing well. So having a back-up striker with a potential like Zagsy, you know, obviously we've got with Charleston, we've got a place centre forward, so there's not, you know, an immediate need for him to play if Dominic is going to get the wages from Charleston. You can play, and obviously the massinations, we move everyone round, maybe, you know, we will be, we've got options there anyway to play wide. So, yeah, it represents a good option. I think I've talked about this before, Marcell, but this is something that we should probably look to do more often. You know, there's so many, so many places in these, you know, what we call the elite teams, and good players slip through the cracks because they just can't get games and they want to move and it's up to evidence to find those and bring them to the club because we could be the ones that benefit from it. Really an eight million outlaying, you know, in the current market, at the end of it, more than really be a bad investment. I think we've seen before with Luchman and Vlastage who never waved out an evidence. They were easy to flip in the long run because they were younger, and they still had that potential tag on them. So, yeah, I think it's a win-win from that point. I just think the expectations of the fans need to be turned slightly. Definitely. I think we're all looking for that because we're where evidence are in the Premier League at the moment. We're all looking for that little bit of boost for the second half of the season. And there's not to say, this isn't to say that's it. He couldn't come in and maybe get four or five goals because he just might be that player in the right place at the right time that gets us an important goal. So, we're not saying he wouldn't produce it if he'd come in. I mean, what we're saying is it would be one where it's a little bit of a flip of a coin really as to whether he'll make the impact or he won't. But, you know, if everything were to trade out Moise Keane, you know, sell Moise Keane for a big amount of money, and we got to say, not to replace Moise Keane, but as an understudy striker, then that would be sensible because we'd still have a young, you know, physically ready centre forward who's learning his trade, you know, in the club. So Moise Keane, go on out. We'd still have that as a backup. But do you think just finally on this bit, then, do you think that if we did get to Xeon, it might be more of an idea for Everton or they may be thinking like this to get to concentrate then on a wide player as well? Because the Charleston can play through the middle, if they were to get to Xeon, say, then Everton's attention could really go to maybe another player who can play off the right or off the left. You know what I'm going to say, obviously Mr Bailey, who I'd love. But Raphael Lau, who's someone we rate me and you really, like you've done quite a bit on the channel over the last couple of years, he's one who's been touted the 26 million Milan, apparently ready to deal a 26 million, I don't know how accurate that is, but he's one who could play right away across the front three as well, isn't he? So a guess that would enable Everton to still have a Dominic Halvitt-Lewman type profile there in Zerchie, but able to have another attacker who can play and who's a bit more versatile, say? Yeah, I think that should be the plan. I think that Everton need that face-atility in the squad. We've talked over it before. I don't want to sign too many specials because when you have to look to the bench for options, there's only so many finite things you can do. With Leo, Leo can play centre forward, obviously left, right. You know, I've said before, I've raised him at the time. I thought he was more ready than Moschee was at the time. But at the thing with Leo, I think a left wing, it might be the order of the day. Obviously, a lot depends on Alex and what he does till the end of the season. Now, if he can maintain the level he showed recently, then he may be the backup to hammer centre in next season, which is good. And then you find someone who can play left while the Charleston plays centre, or if he can play righty in another formation. Then obviously, Everton in a much better position there, and then the manager then can have options to each different game, depending on the opponent, which is what you want to do really at the end of the day, isn't it? I think, finally, on Everton 4, we've just moved on to another couple of other transfers. Everton will be looking to off-load Bernard, whether it happens in the next five days or whether it's in the summer months. And they're going to have to replace that, aren't they? Because, you know, I don't think Anthony Gordon at this moment in time is ready to be back on a regular basis. So Everton would have to look for that anyway, and someone who can, like a law or a baili, who can play either side, that would then free up those, even with a woby, because ideally, we want a woby to continue to improve anyway. So ideally then, it takes the pressure off hammers as well, wouldn't it? Because he wouldn't have to necessarily play every game, and you'd be able to fresh in that front three up quite regularly. And that's what the teams who get into the Champions League and do well, or Europa League, and go deep in the Cups, that's what they do well, don't they? They've got that fluidity in the front positions to be able to mix it up? Exactly, you've got the space, you've got Bail, Beguine, Mora, they've got different players in the government, you've got Man United, Swabrail, Kevani, Rashford, Marshall, Greenwood. So we need those sort of options, and obviously all them can play across the front as well. So yeah, it's really imperative that Everton get a fluid squad where they can move things about rather than signers, a backup striker like Fernando Llorenti, whilst it's hot and we've played every thousandth game forward and it was taking a big wage. Everton needs to be smart, we just need to be a smart club and I think that's the best way to go. Definitely. A couple of transfers just generally bouncing around, obviously I think we've been talking off camera before, it's very quiet isn't it, there's not much sloshing around in terms of money. In January it's tended over the last few years anyway and the spendings got less. I know Bruno Fernandez went for 70 million and I know Virgil van Dijk a couple of years ago went for the same, but in general the spendings January has come down a lot. But particularly what we're in the middle of now with obviously with Covid and everything, it was always going to be a quiet month anyway, clubs posting big losses all over the gaff. But a couple of things that are hanging around are obviously Martin Aldegard, he was a player who was linked with Everton the other day as a potential loan destination on Leicester City, he's joined Arsenal. Good player, good attacking player, I guess the only thing for him is can he cope with the physicality of the Premier League in a short period of time. The talks that Rayon had did one and back in the summer he's not, there's no plans to let him go and it's literally just to give him some game time and experience. So he's a nice player isn't he Aldegard? Yeah it really creates a footballer vision passing, obviously creates a great space for himself in chipping the goals, I think Arsenal really needed that sort of player. I think it's done me wrong, I love Emile Smith, I think he's a fantastic young player. I suppose it just adds to their options now, particularly fan of Arsenal. The last one was alright, it's the fella in charge but yeah, go on. But for them they were going to buy one in the summer anyway so to bridge that gap between the summer without having to rely on a 20-year-old, it's smart business really. Aldegard's probably going to have to have a look in the summer because they've signed a lot of young players that just don't seem to break through, obviously Yovic has come back to Eintracht Frankfurt. Zeddan seems reluctant to blood these young players a lot so I think you may see players leaving much in the summer and reportedly they might need to sell a couple so Aldegard might be available in the summer for some so it's a good audition for him in the Premier League. Definitely, unless Zeddan leaves in the summer which may happen as well. Another one, Jesse Lingard, a lot of Evertonians just coward them when I said that. Looks as though Westam are very interested in him, seems like a Westam signing to me but Westam are interested in West Brommer trying to get him as well on loan. A good loan signing for those two clubs he's to eat. Look like he was going to be decent for United without being amazing but over the last 12 months he's just disappeared into nothing hasn't he? The issue with Jesse Lingard is his social media presence, a lot of people think that's all he cares about in his fashion line and I think maybe he lost sight of it, I'm not going to make assumptions about the player.  Moises took those players on before on Tether and Pinar, had tough times in the previous clubs and re-energised them. I think Lingard knows the Premier League, I think the summer before the World Cups, the season before sorry, 17-18 had a pretty good season for Man United. I think if he can get back to those levels then he'd be interested in Montfamoy's. It's a risk though as I say, I suppose he has a reputation for being unserious in the dressing room. If Moises thinks he can handle it, I think then they'll take it on. It's a risky one but it might work out if he gets back to that level. Definitely, Deli Alley looks like he's staying at Spare's. Marino said he doesn't expect him to go, which doesn't really surprise. Now he's linked to that but he's only really going to be PSG, wasn't it, pot of tea. You know whether he'd take his chance but it looks like he's not going anyway. So everything else is really quite quiet. Wolves are still waiting for William Hosey's work permit. I think he'd be a good sign and for them they haven't got a target man. I know it's hit and miss whether or not he'll settle in the Premier League but they're lacking on the upfront because they've obviously ralled him and this is injury. So it's going to be interesting for you to see whether anything actually happens. Now on this show we've been asking you to get in touch with us using the hashtag fanline as part of the Snickers Protein sponsorship. We've been asking you to get in touch with your comments over the old using the hashtag fanline and a few of you have so it's over to Ned. We've had a tweet from at dunk39. He says, Given the fact that Cardi is back and Pochettino was notorious for high expectations regarding dedication and discipline, has Keane reached his peak value for a sale? If he falls out of the picture and his value plummets, do we keep him as a backup? I mean that's a very interesting one isn't it? We've spoke, me and Pead have certainly spoke about the Moise Keane situation and trying to sell him at the height of his powers. Pochettino's in there and the Cardi's back. Moise Keane hasn't had as many minutes the last couple of games. But unless PSG put the silver briefcase on the table with the money in it, there's not really much we can do at the moment is there? No, we can't. I spoke about this from Moise Keane. There's not really much we can do in terms of value. There's not a lot of team suspending in this window, so we can do this for real. If you have a type of powers, I'm going to spend 35, 40 million, whatever that is at one forum in this window. It all depends on Moise Keane. I think he'll have suitors in the summer when he's shown that he's at a certain level. So it's just up to everyone to find the right deal and suitors. I doubt he stays during this week because he's up on the main sale of the last summer. We probably need one or two players out just to start bringing players in. Yeah, definitely. I think we all want them to have a really good second half of the season. So that we get a couple of others, you've got someone else interested and then look for what deal we can get the best. Because I don't think he'll want to come back to Everton without being guaranteed to play games. And I don't think Everton will want to guarantee him that thing because obviously we've got them. So it's going to be interesting. Yeah, Ned, next. Attoffi underscore D says, is there a player 30 plus in the Premier League that won't mind bench warming, but be good enough quality to squad rotate when needed with DCL till the end of the season? Andy. You think about it if it's for a load. I can only really think I like Joshua King and they wouldn't loan him to us because his contract's up in the summer. And he wants big money. I can't really think of anyone in the Premier League who's sat on someone's bench not playing, can you? Who would help us? I also, you don't want to make a sign for the sake of the sign. I know people are at the end of the territory in Towsonbuff in the days. He's an international, he's experienced, he's scored a couple of goals in this league. He's not the worst option, there's much worse options around. And he's got the assets we've got to pay for him in any way. So, yeah, I wouldn't just go out and get a player for the sake of it. That would be my place anyway. I can't see any anyway. That would really make that much of a difference to, like you say, a better than Towson, I guess, at the moment. Probably is in Wales football, but it's whether Evan would want to make that decision right now. I've seen people call him for Ed and Jaco, but I don't have the big money and all. Go on, Ned. At Satoshi Corners says, if Towson and Kenny are sold in this window, should we put that money towards a move for Danny Ings in the summit? He's stolen a contract there. Andy, go on. Okay, people are usually feel about things and they're prepared to be going to cry on and say this. I think Danny Ings is a great player. I just think for Evan, and how much Danny Ings wants in the lengthy contract he wants, but his injury is just going to get a massive risk. It'll be wrong in the short term, it could wake up. Is he going to play every game for Evan? Maybe, I don't know. I think he suits the system. I think he'd be quite foolish to be passing the whole system. I think he's going to make his name. He's been getting chances there. I wouldn't go for Danny Ings. You know what people would do because he's got a proven goal scorer on their couple. Then he's worried me badly. Yeah, it's 28. He's had two really bad injuries. He's obviously a good player. There's no question about it and also the net is, but Evan would have to play 4-4-2 with him because you wouldn't choose Danny Ings over Dominic. Well, I wouldn't choose Danny Ings over Dominic all the living to lead the line for Evan. You know, as a one, definitely no. If Evan played 4-4-2 and you had Richard Charles in one side and you got someone else on the other who was equally hardworking, maybe, but I think I want one that can go right away across the front line. Because obviously that's Evan at the strongest playing that way, it seems. No, he's a good player, there's no question about it. Certainly, if we manage to sell toxin on Bernard and put that money towards summer planning really, isn't it? That seems the most sensible thing now, doesn't it? Because we've seen what the manager's done with this team, Andy, with 3 or 4 new signings. You think imagine 3 or 4 new ones again this summer who it is players or certainly players who are better than what we've got. It means that next season could be exciting as well, couldn't that Evan could be pushing for those top places again next season? Yeah, you're getting 4 or 5 players in the summer. I'm on a stronger squad there with multiple options in case of injury. So, yeah, I think that would be much, you know, you're getting this situation now where you can be much more consistent and you're not, you know, living in Zion by who's injured and who's not injured and I think that's where it needs to be. And I think that's the plan. I think this season's made the Europa League next season and has pushed on for the Champions League and four good signs will do that for you. I think it's got big thanks to Andy for joining me today. Don't forget to check out the Snickers Pro team deadline day on Ball Street on their YouTube channel. Four hours of live action there. Me and Ped will be on there at some stage as well. So make sure you don't miss out on that one. And make sure you give this video a thumbs up, subscribe if you haven't. And if you want more videos, join us over on Patreon. See you later.


My name is Brandon Ruth and I'm the Director of Operations for the Atlanta Falcons. We have a big trip coming up across the pond, obviously, a game in London versus the New York Jets, so my role is pretty much to get our entire operation, our team, all of our equipment over from Atlanta all the way over to London and get ready to play a football game. It's not as simple as, you know, us going to Carolina or New Orleans, you know, there's a lot more paperwork, a lot more things that we have to file to take everybody over there.  And then obviously as you get closer, it revs up a lot, but, you know, you're pretty much thinking about this trip from, you know, the moment, you know, the last season ends to where we are now.  And then, you know, in terms of cargo, you know, we'll have about seven thousand pounds underneath the plane. But then the other thing with a trip like this one, we have to send close to almost twenty thousand pounds worth of equipment over to London on an ocean-free shipment. So that's equipment that we don't see for months because that's to get loaded into a shipping container, get on a boat, and then we'll go all the way over there. You know, obviously, like, we want to leave with the wind, but, you know, in order for us to leave with the wind, you know, I want to make sure that we make the trip as seamless as possible and by doing that, it's really making sure the players, coaches stay on that same schedule that they're accustomed to. So we want to make sure that everybody sleeps, everybody gets the rest that they need on that trip. Luckily enough, Bose was able to provide us with noise masking sleep buds, so that way they can utilize those, get some good sleep.


Okay, so contrary to what I said in the last video, it has been a very active discussion in the Patreon comments about what episodes I should watch So I think I'm watching everything except 73 and 74 Those were the two that were kind of universally agreed upon that I should skip at least from what I saw But we're back today with Dragon Ball Super Episode 70 And I believe this is the baseball episode that decent amount of you asked me to watch don't know much about it except the Fact that it's a baseball episode I'm pretty sure baseball is the sport that Yamcha plays because I did a video on the non-reaction channel where I asked people that at TwitchCon what sport does Yamcha play? Come on. Do you know what sport Yamcha plays in Dragon Ball Z? It's always on the ground. I don't know where you play Okay, thank you for your time. Oh my god, but yeah, I'm not gonna waste too much time If you need a channel, don't forget to drop a sub and let's hop into it Okay, but not wasting any time I guess Friendship between your universe We're gonna chop a here about baseball, man. It's big in Japan though, right? I agree. I agree and where exactly are you suggesting we play this ball of ball of bases You can just build another arena or field or something Let's go. Wait, so what are the teams? He fell right into my trap. Of course.  We'll just say good game and celebrate with a big feast It's a win-win scenario. He loses. He gets to eat. He wins.  I kind of wanted to sit in there was a tireless to hear his questions Oh my goodness. This is gonna be so cozy.  Even Winnie the Pooh is there So Vegeta's on the other team. Oh, it's not here either. Let's all bow and say good game Let's go universe six universe six I'm so freaking losing the rest of the team. I'm worried about bro There's no way. Why do you have to close Krillin? To the test this is such a wholesome episode Did none of you research, I guess it was like a last minute thing These are siren. I call for time. Oh classic baseball. All right. Here we go I don't care if he is a destroyer Goku. You cannot let me throw that ball at maximum power Yeah, these characters are too strong for baseball Okay, dude.  Chapa, you know what you asked for So are we rebuilding the stadium? What happened to Yamcha Thanks guys Okay, take it down a notch I'm changing my picture at the showers Goku. Goku's already out my lord. Are you talking about the starting picture cannot be changed until He's gonna start beating up Goku Not too. Oh, he's gonna he's gonna over correct and throw it way too soft Oh no, here we go There's no way to just wait for it to get the choppa Kids Oh my god, I got pooped on Bubbin in man. Here we go. Okay, but if he misses it's gonna be humiliating Bubbin in man, no! I can't I can't I can't Okay, here we go. I feel like I'm getting some mixed signals There's no in between I guess with the difference. There you go. Yes. This is gonna be big That looked perfect. It was but unfortunately chapa is pretty talented honestly at batting I'm right. Wait crow is gonna fly up and grab it. Is that allowed? Oh, is that allowed? It wasn't destructive My goodness It was creative true again. Couldn't you just fly up and grab it though?  You're both the same If trunks hadn't stepped in that would have been a home run. So it's Goku getting swapped. Oh, Yamcha's pitching. Yes Let the Yamcha show you what it's like. The Yamcha. All right, but oh shoot.  This is how it's done. This is your moments. You're clowned consistently throughout the show This is where you prove those haters wrong Oh my god, it's beautiful Oh, I thought you just flipped them off. Wait, what? Is that allowed? Ah, the rulebook wouldn't say anything about that.  Oh, yeah, I forgot Vegeta's master. He's trying to prove it to him Sorry cabba Nobody escapes the wolf Thanks virus He's having his moment. This is so sweet.  He's gonna injure their best pitcher It's gonna be coming back. All right. His pitching skills are solid.  Oh my gosh No, it's like them for that Yamcha want the first baseball that's your loss Vegeta The beauty of baseball. Okay. It's time to give this. All right. Here goes Goku If Goku hits the ball, he's not gonna know what to do. He's he's gonna be like, okay. What now nobody told him to run Oh deals Mio. They're gonna destroy this place I can't watch The ultimate strike He's putting his all into it. What are you gonna do catch it on the way back? What? Okay, that no, that's just not fair. Whis Whis it's about their fighting Saiyan spirits against each other He's gonna find out what I still don't understand the rules. Oh my god.  You'll never make it. Go back. Oh my god. It's chaos. This is intense, man Oh There's no way they're doing my boy Yamcha like this man. There's no way That counts as obstructing the runner.   Why would that make it any better just to wake him up? You see that player over there who looks like a robot. Oh my god. He's gonna tell him to insult him Oh, no, that's a better idea. I don't know why I thought about that Yo, I'm just looking at the sky. Come on, buddy. You got this. All right above magetta.  They literally made this episode just to beat Yamcha This is so mean. You have to be holding the ball. Yep Should have read the rules chamba He only needs one more run, but of course this is just the sort of player you'll get with a lousy manager What do you mean? He's got spirit The big boys My god, what is happening? Oh my god, it's two destroyers going head to head What did I say? They haven't even fought. They're just yelling. Oh, no You weenie They're just running back and forth. Everybody jump on the goku My god, man. I wanted Yamcha to be able to make it to home base. Have they ever fought like this before? Oh, there we go Thank you. It's one of the greatest taboos of the cosmos for destroyers to it's a taboo I guess it makes sense if that much destruction comes with it We hereby rule you're in gross violation and oh, it's just the game's over seventh universe team wins one run to nothing Yeah, wait, what? See for yourself lord. Champa look down at home plate. Oh my god There's no way they brought that post back bro. There's no way He stole whole shot. What a callback This is the greatest episode of anime of all time. My god Dude, I would say I would watch a whole season of this as a baseball anime man Tell me there's a rematch at some point, please Dog I love how direct they were with that call about the it rings a painful bell Oh my gosh The the returning characters was a nice surprise Yamcha being sort of the main focus was an amazing surprise The whole episode overall was fantastic And we got to see that destroyers almost start sparring in a little tease of what happens when they do Because we've seen them arguing what not before but never really start throwing fists at each other But another really solid filler episode being that in filler episodes There's no consequences to an extent So you can bring these characters back and know their tropes and whatnot and just kind of have fun with them Because it's been in for episode 70 track ball super do drop us some of the channel if you're new and I'll catch you in the next one base base