be impossible! This is a wretched beginning indeed. My sole dependent was on you, and I am sure nobody else will believe me if you do not. Yet indeed I am in earnest. I speak nothing but the truth. He still loves me, and we are engaged. Jane looked at her doubtingly. Oh, Lizzy! It cannot be! I know how much you dislike him. You know nothing of the matter. That is all to be forgot. Perhaps I did not always love him so well as I do now. But in such cases as these a good memory is unpardonable. This is the last time I shall ever remember it myself. Miss Bennet still looked all amazement. Elizabeth again and more seriously assured her of its truth. Good Heaven! Can it really be so? Yet now I must believe you! cried Jane. My dear, dear Lizzy! I would—I do congratulate you. But are you certain? Forgive the question. Are you quite certain that you can be happy with him? There can be no doubt of that. It is settled between us already that we are to be the happiest couple in the world. But are you pleased, Jane? Shall you like to have such a brother? Very, very much. Nothing could give either Bingley or myself more delight. But we considered it. We talked of it as impossible. And do you really love him quite well enough? Oh, Lizzy! Do anything rather than marry without affection.  Oh, yes. You will only think I feel more than I ought to do when I tell you all. What do you mean? Why, I must confess that I love him better than I do Bingley. I am afraid you'll be angry. My dearest sister! Now be serious. I want to talk very seriously. Let me know everything that I am to know without delay. Will you tell me how long you have loved him? It has been coming on so gradually that I hardly know when it began. But I believe I must date it from my first seeing his beautiful grounds at Pemberley. Another entreaty that she would be serious, however, produced the desired effect, and she soon satisfied Jane by her solemn assurances of attachment. When convinced on that article, Miss Bennet had nothing further to wish. Now I am quite happy, said she. For you be as happy as myself. I always had a value for him. Were it for nothing but his love of you, I must always have esteemed him. But now, as Bingley's friend and your husband, there can only be Bingley and yourself more dear to me. But, Lizzy, you have been very sly, very reserved with me. How little did you tell me of what passed at Pemberley and Lambton. I owe all that I know of it to another, not to you. Elizabeth told her the motives of her secrecy. She had been unwilling to mention Bingley, and the unsettled state of her own feelings had made her equally avoid the name of his friend. But now she would no longer conceal from her his share in Lydia's marriage. All was acknowledged, and half the night spent in conversation. Good gracious! cried Mrs. Bennet as she stood at a window the next morning. If that disagreeable Mr. Darcy is not coming here again with our dear Bingley, what can he mean by being so tiresome as to always be coming here? I had no notion, but he would go with shooting, or something or other, and not disturb us with his company. What shall we do with him? Lizzy, you must walk out with him again that he may not be in Bingley's way. Elizabeth could hardly help laughing at so convenient a proposal, yet was really vexed that her mother should be always giving him such an apathit. As soon as they entered, Bingley looked at her so expressively, and shook hands with such warmth, as left no doubt of his good information, and he soon afterwards said aloud, Mrs. Bennet, have you no more lanes hereabouts in which Lizzy may lose her way again today? I advise Mr. Darcy and Lizzy and Kitty, said Mrs. Bennet, to walk to Oakham Mount this morning. It is a nice long walk, and Mr. Darcy has never seen the view. It may do very well for the others, replied Mr. Bingley, but I am sure it will be too much for Kitty. Won't it, Kitty? Kitty owned that she had rather stay at home. Darcy professed a great curiosity to see the view from the mount, and Elizabeth silently consented. As she went upstairs to get ready, Mrs. Bennet followed her, saying, I am quite sorry, Lizzy, that you should be forced to have that disagreeable man all to yourself. But I hope you're not minded. It is all for Jane's sake, you know, and there is no occasion for talking to him, except just now and then. So do not put yourself to inconvenience. During their walk it was resolved that Mr. Bennet's consent should be asked in the course of the evening. Elizabeth reserved to herself the application for her mother's. She could not determine how her mother would take it, sometimes doubting whether all his wealth and grandeur would be enough to overcome her abhorrence of the man. But whether she were violently set against the match, or violently delighted with it, it was certain that her manner would be equally ill-adapted to do credit to her sense, and she could no more bear that Mr. Darcy should hear the first raptures of her joy than the first vehemence of her disapprobation. In the evening, soon after Mr. Bennet withdrew to the library, she saw Mr. Darcy rise also and follow him, and her agitation on seeing it was extreme. She did not fear her father's opposition, but he was going to be made unhappy, and that it should be through her means that she, his favourite child, should be distressing him by her choice, should be filling him with fears and regrets and disposing of her, was a wretched reflection, and she sat in misery till Mr. Darcy appeared again. When looking at him, she was a little relieved by his smile. In a few minutes he approached the table where she was sitting with Kitty, and while pretending to admire her work, said in a whisper, Go to your father, he wants you in the library. She was gone directly. Her father was walking about the room looking grave and anxious. Lizzie! said he, What are you doing? Are you out of your senses to be accepting this man? Have you not always hated him? How earnestly did she then wish that her former opinions had been more reasonable, her expressions more moderate? It would have spared her from explanations and professions which it was exceedingly awkward to give, but they were now necessary, and she assured him with some confusion of her attachment to Mr. Darcy. Or, in other words, you are determined to have him. He is rich to be sure, and you may have more fine clothes and fine carriages than Jane, but will they make you happy? Have you any other objection? said Elizabeth, then your belief of my indifference. None at all. We all know him to be a proud, unpleasant sort of man, but this would be nothing if you really liked him. I do. I do like him.  I love him. Indeed, he has no improper pride. He is perfectly amiable. You do not know what he really is. Then pray do not pain me by speaking of him in such terms. Lizzie! said her father. I have given him my consent. He is the kind of man indeed to whom I should never dare refuse anything which he condescended to ask. I now give it to you, if you are resolved on having him. But let me advise you to think better of it. I know your disposition, Lizzie. I know that you could be neither happy nor respectable unless you truly esteemed your husband, unless you looked up to him as a superior. Your lively talents would place you in the greatest danger in an unequal marriage. You could scarcely escape discredit and misery. My child, let me not have the grief of seeing you unable to respect your partner in life. You know not what you are about. Elizabeth, still more affected, was earnest and solemn in her reply. And at length, by repeated assurances that Mr. Darcy was really the object of her choice, by explaining the gradual change which her estimation of him had undergone, relating her absolute certainty that his affection was not the work of a day, but had stood the test of many months' suspense, and enumerating with energy all his good qualities, she did conquer her father's incredulity and reconcile him to the match. Well, my dear! said he when she ceased speaking. I have no more to say. If this be the case, he deserves you. I could not have parted with you, my Lizzie, to any one less worthy. To complete the favourable impression, she then told him what Mr. Darcy had voluntarily done for Lydia. He heard her with astonishment. This is an evening of wonders indeed. And so Darcy did everything. Made up the match, gave the money, paid the fellow's debt, and got him his commission. So much the better. It will save me a world of trouble and economy. Had it been your uncle's doing, I must and would have paid him. But these violent young lovers carry everything their own way. I shall offer to pay him to-morrow. He will rant and storm about his love for you, and there will be an end of the matter. He then recollected her embarrassment a few days before on his reading Mr. Collins' letter, and after laughing at her some time, allowed her at last to go, saying as she quitted the room, If any young men come for Mary or Kitty, send them in, for I am quite a leisure. Elizabeth's mind was now relieved from a very heavy weight, and after half an hour's quiet reflection in her own room, she was able to join the others with tolerable composure. Everything was too recent for gaiety, but the evening passed tranquilly away. There was no longer anything material to be dreaded, and the comfort of ease and familiarity would come in time. When her mother went up to her dressing-room at night, she followed her and made the important communication. Its effect was most extraordinary, for on first hearing it, Mrs. Bennet sat quite still and unable to utter a syllable. Nor was it under many, many minutes that she could comprehend what she heard, though not in general backward to credit what was for the advantage of her family, or that came in the shape of a lover to any of them. She began at length to recover, to fidget about in her chair, get up, sit down again, wonder and bless herself. God gracious, Lord bless me! Only think, dear me, Mr. Darcy! Who would have thought it? And is it really true? Oh, my sweetest Lizzie, how rich and how great you will be! What pin-money, what jewels, what carriages you will have! James is nothing to it, nothing at all! I am so pleased, so happy! Such a charming man, so handsome, so tall! Oh, my dear Lizzie, pray, apologize, my having disliked him so much before. I hope you will overlook it. Dear, dear Lizzie! A house in town, everything that is charming! Three daughters married, ten thousand a year! Oh, Lord, what will become of me? I shall go distracted! This was enough to prove that her approbation need not be doubted, and Elizabeth rejoicing that such an effusion was heard only by herself, soon went away. But before she had been three minutes in her own room, her mother followed her. My dearest child! She cried, I can think of nothing else, ten thousand a year and very likely more! Tis as good as a Lord! And a special licence! You must and shall be married by a special licence! But my dearest love, tell me what dish Mr. Darcy is particularly fond of, that I may have it to-morrow! This was a sad omen of what her mother's behaviour to the gentleman himself might be, and Elizabeth found that, though in the certain possession of his warmest affection, and secure of her relations' consent, there was still something to be wished for. But the morrow passed off much better than she expected, for Mrs. Bennet luckily stood in such awe of her intended son-in-law, that she ventured not to speak to him, unless it was in her power to offer him any attention or mark her deference for his opinion. Elizabeth had the satisfaction of seeing her father taking pains to get acquainted with him, and Mr. Bennet soon assured her that he was rising every hour in his esteem. I admire all my three sons-in-law highly, said he. Wickham perhaps is my favourite, but I think I shall like your husband quite as well as James. Pride and Prejudice by Jane Austen Chapter 60 Elizabeth's spirit soon rising to playfulness again, she wanted Mr. Darcy to account for his having ever fallen in love with her. How could you begin? said she. I can comprehend your going uncharmingly when once you had made a beginning, but what could set you off in the first place? I cannot fix on the hour, or the spot, or the look, or the words which laid the foundation. It is too long ago. I was in the middle before I knew that I had begun. My beauty you had early withstood, and as for my manners, my behaviour to you was at least always bordering on the uncivil, and I never spoke to you without rather wishing to give you pain than not. Now be sincere. Did you admire me for my impertinence? For the liveliness of your mind I did. You may as well call it impertinence at once. It was very little less. The fact is that you were sick of civility, of deference, of officious attention. You were disgusted with the women who were always speaking and looking and thinking for your approbation alone. I roused and interested you because I was so unlike them. Had you not been really amiable, you would have hated me for it. But in spite of the pains you took to disguise yourself, your feelings were always noble and just, and in your heart you thoroughly despised the persons who so assiduously courted you. There, I have saved you the trouble of accounting for it, and really all things considered I begin to think it perfectly reasonable. To be sure you knew no actual good of me, but nobody thinks of that when they fall in love. Was there no good in your affectionate behaviour to Jane while she was ill at another field? Tearist Jane! Who could have done less for her? But make a virtue of it by all means. My good qualities are under your protection, and you are to exaggerate them as much as possible, and in return it belongs to me to find occasions for teasing and quarrelling with you as often as may be, and I shall begin directly by asking you what made you so unwilling to come to the point at last, what made you so shy of me when you first called, and afterwards dined here? Why, especially when you called, did you look as if you did not care about me? Because you were grave and silent and gave me no encouragement. But I was embarrassed, and so was I. You might have talked to me more when you came to dinner. A man who had felt less might. How unlucky that you should have a reasonable answer to give, and that I should be so reasonable as to admit it. But I wonder how long you would have gone on if you had been left to yourself. I wonder when you would have spoken if I had not asked you. My resolution of thanking you for your kindness to Lydia had certainly great effect. Too much, I am afraid, for what becomes of the moral of our comfort springs from a breach of promise. For I ought not to have mentioned the subject. This will never do. You need not distress yourself. The moral be perfectly fair. Lady Catherine's unjustifiable endeavours to separate us were the means of removing all my doubts. I am not indebted for my present happiness to your eager desire of expressing your gratitude. I was not in a humour to wait for any opening of yours. My aunt's intelligence had given me hope, and I was determined at once to know everything. Lady Catherine has been of infinite use, which ought to make her happy, for she loves to be of use. But tell me, what did you come down to Netherfield for? Was it merely to ride to Longbourn and be embarrassed, or had you intended any more serious consequence? My real purpose was to see you, and to judge, if I could, whether I might ever hope to make you love me. My avowed one, or what I vowed to myself, was to see whether your sister was still partial to Bingley, and if she were, to make the confession to him which I have since made. Shall you ever have courage to announce to Lady Catherine what is to befall her? I am more likely to want more time than courage, Elizabeth, but it ought to be done, and if you will give me a sheet of paper, it shall be done directly. And if I had not a letter to write myself, I might sit by you and admire the evenness of your writing, as another young lady once did. But I have an aunt, too, who must not be longer neglected. From an unwillingness to confess how much her intimacy with Mr. Darcy had been overrated, Elizabeth had never yet answered Mrs. Gardner's long letter. But now, having that to communicate which she knew would be most welcome, she was almost ashamed to find that her uncle and aunt had already lost three days of happiness, and immediately wrote as follows. I would have thanked you before, my dear aunt, as I ought to have done, for your long-kind satisfactory detail of particulars. But to say the truth, I was too cross to write. You supposed more than really existed.  And unless you believe me actually married, you cannot greatly err. You must write again very soon, and pray some a great deal more than you did in your last. I thank you again and again for not going to the lakes. How could I be so silly as to wish it? Your idea of the ponies is delightful. We will go round the park every day. I am the happiest creature in the world. Perhaps other people have said so before, but not one with such justice. I am happier even than Jane. She only smiles. I laugh. Mr. Darcy sends you all the love in the world that he can spare from me. You are all to come to Pemberley at Christmas. Yours, etc. Mr. Darcy's letter to Lady Catherine was in a different style, and still different from either was what Mr. Bennet sent to Mr. Collins, in reply to his last. Dear sir, I must trouble you once more for congratulations. Elizabeth will soon be the wife of Mr. Darcy. Can so, Lady Catherine, as well as you can. But if I were you, I would stand by the nephew. He has more to give. Yours sincerely, etc. Miss Bingley's congratulations to her brother on his approaching marriage were all that was affectionate and insincere. She wrote even to Jane on the occasion to express her delight and repeat all her former professions of regard. Jane was not deceived, but she was affected, and though feeling no reliance on her could not help writing her a much kinder answer than she knew was deserved. The joy which Miss Darcy expressed on receiving similar information was as sincere as her brother's in sending it. Four sides of paper were insufficient to contain all her delight and all her earnest desire of being loved by her sister. Before any answer could arrive from Mr. Collins, or any congratulations to Elizabeth from his wife, the long-born family heard that the Collins's were come themselves to Lucas Lodge. The reason of this sudden removal was soon evident. Lady Catherine had been rendered so exceedingly angry by the contents of her nephew's letter that Charlotte, really rejoicing in the match, was anxious to get away till the storm was blown over. At such a moment the arrival of her friend was a sincere pleasure to Elizabeth. Though in the course of their meeting she must sometimes think the pleasure dearly bought when she saw Mr. Darcy exposed to all the parading and obsequious civility of her husband. He bore it, however, with admirable calmness. He could even listen to Sir William Lucas when he complimented him on carrying away the brightest jewel of the country and expressed his hopes of their all meeting frequently at St. James's with very decent composure. If he did shrug his shoulders, it was not till Sir William was out of sight. Mrs. Phillips's vulgarity was another and perhaps a greater tax on his forbearance, and though Mrs. Phillips, as well as her sister, stood in too much awe of him to speak with the familiarity which Bingley's good humour encouraged, yet whenever she did speak she must be vulgar. Nor was her respect for him, though it made her more quiet, at all likely to make her more elegant. Elizabeth did all she could to shield him from the frequent notice of either and was ever anxious to keep him to herself and to those of her family with whom he might converse without mortification, and though the uncomfortable feelings arising from all this took from the season of courtship much of its pleasure, it added to the hope of the future, and she looked forward with delight to the time when they should be removed from society so little pleasing to either, to all the comfort and elegance of their family party at Pemberley. CHAPTER 61 Happy for all her maternal feelings was the day on which Mrs. Bennet got rid of her two most deserving daughters, with what delighted pride she afterwards visited Mrs. Bingley and talked of Mrs. Darcy may be guessed. I wish I could say for the sake of her family that the accomplishment of her earnest desire in the establishment of so many of her children produced so happy an effect as to make her a sensible, amiable, well-informed woman for the rest of her life, though perhaps it was lucky for her husband, who might not have relished domestic felicity in so unusual a form, that she was still occasionally nervous and invariably silly. Mr. Bennet missed his second daughter exceedingly. His affection for her drew him oftener from home than anything else could do. He delighted in going to Pemberley, especially when he was least expected. Mr. Bingley and Jane remained at Netherfield only a twelve month. So near a vicinity to her mother and maritain relations was not desirable even to his easy temper or her affection at heart. The darling wish of his sisters was then gratified. He bought an estate in a neighboring county to Darbyshire, and Jane and Elizabeth, in addition to every other source of happiness, were within thirty miles of each other. Kitty, to her very material advantage, spent the chief of her time with her two elder sisters. In society so superior to what she had generally known, her improvement was great. She was not of so ungovernable a temper as Lydia, and removed from the influence of Lydia's example, she became, by proper attention and management, less irritable, less ignorant, and less insipid. From the further disadvantage of Lydia's society, she was of course carefully kept, and though Mrs. Wickham frequently invited her to come and stay with her with the promise of balls and young men, her father would never consent to her going. Mary was the only daughter who remained at home, and she was necessarily drawn from the pursuit of accomplishments by Mrs. Bennet's being quite unable to sit alone. Mary was obliged to mix more with the world, but she could still moralize over every morning visit, and as she was no longer mortified by comparisons between her sister's beauty and her own, it was suspected by her father that she submitted to the change without much reluctance. As for Wickham and Lydia, their characters suffered no revolution from the marriage of her sisters. He bore with philosophy the conviction that Elizabeth must now become acquainted with whatever of his ungratitude and falsehood had before been unknown to her, and in spite of everything, was not wholly without hope that Darcy might yet be prevailed on to make his fortune. The congratulatory letter which Elizabeth received from Lydia on her marriage explained to her that, by his wife at least, if not by himself, such a hope was cherished. The letter was to this effect. My dear Lizzy, I wish you joy. If you love Mr. Darcy half as well as I do, my dear Wickham, you must be very happy. It is a great comfort to have you so rich, and when you have nothing else to do, I hope you will think of us. I am sure Wickham would like a place at court very much, and I do not think we shall have quite money enough to live upon without some help. Any place would do, of about three or four hundred a year, but, however, do not speak to Mr. Darcy about it, if you would rather not. Yours, etc. As it happened that Elizabeth had much rather not, she endeavored in her answer to put an end to every entreaty and expectation of the kind. Such relief, however, as it was in her power to afford, by the practice of what might be called economy in her own private expenses, she frequently sent them. It had always been evident to her that such an income as theirs, under the direction of two persons so extravagant in their wants, and heedless of the future, must be very insufficient to their support, and whenever they changed their quarters, either Jane or herself were sure of being applied to for some little assistance towards discharging their bills. Their manner of living, even when the restoration of peace dismissed them to a home, was unsettled in the extreme. They were always moving from place to place in quest of a cheap situation, and always spending more than they ought. His affection for her soon sunk into indifference. Hers lasted a little longer, and in spite of her youth and her manners, she retained all the claims to reputation which her marriage had given her. Though Darcy could never receive him at Pemberley, yet for Elizabeth's sake he assisted him further in his profession. Lydia was occasionally a visitor there, when her husband was gone to enjoy himself in London or Bath, and with the Bingley, say both of them frequently stayed so long, that even Bingley's good humour was overcome, and he proceeded so far as to talk of giving them a hint to be gone. Miss Bingley was very deeply mortified by Darcy's marriage, but as she thought it advisable to retain the right of visiting at Pemberley, she dropped all her resentment. Was sponder than ever of Georgiana, almost as attentive to Darcy as here to fore, and paid off every arrear of civility to Elizabeth. Pemberley was now Georgiana's home, and the attachment of the sisters was exactly what Darcy had hoped to see. They were able to love each other even as well as they intended. Georgiana had the highest opinion in the world of Elizabeth, though at first she often listened with an astonishment bordering on alarm at her lively, sportive manner of talking to her brother. He, who had always inspired in herself a respect which almost overcame her affection, she now saw the object of open pleasantry. Her mind received knowledge which had never before fallen in her way. By Elizabeth's instructions, she began to comprehend that a woman may take liberties with her husband, which a brother will not always allow, in a sister more than ten years younger than himself. Lady Catherine was extremely indignant on the marriage of her nephew, and as she gave way to all the genuine frankness of her character, in her reply to the letter which announced its arrangement, she sent him language so very abusive, especially of Elizabeth, that for some time all intercourse was at an end. But at length, by Elizabeth's persuasion, he was prevailed on to overlook the offence, and seek her reconciliation, and after a little further resistance on the part of his aunt, her resentment gave way, either to her affection for him, or her curiosity to see how his wife conducted herself, and she condescended to wait on them at Pemberley, in spite of that pollution which its woods had received, not merely from the presence of such a mistress, but the visits of her uncle and aunt from the city. With the gardeners they were always on the most intimate terms. Darcy, as well as Elizabeth, really loved them, and they were both ever sensible of the warmest gratitude towards the persons who, by bringing her into Derbyshire, had been the means of uniting them.


Y'all, I don't even want to take this off. Like, what? To another video, if you're new here, my name is Kyrie. Do not forget to like, comment, and subscribe to this video. So in today's video, we are going to get into a little train haul. I got some pieces from my outfit online. Shout out to my outfit online for partnering with me on this video, y'all. I work with them so many times in the past. I love their clothes. I love their clothes. The fabric hits, okay? When I tell you snatched, the clothes at my outfit online just make you feel so snatched. And they are my in-base, so they already know. They already know what to get a girl's, okay? So if you want to see everything that I got, just keep on watching it. Okay, girls. So the first outfit that I have on is like their signature leggings and their crossback bralette. And this is from their loungewear section. You already know I love me a good loungewear set. And I should have got a small in the leggings, but I kind of was thinking like a loungewear. I want to be cozy and stuff. But it still actually cinches in my waist really nice. But I should have got a small. If I got a small, because it is a little like loose right here, it would have been like snatch. But it still makes the body look good, okay? And I love this blush color. And I love the crossback. I didn't think I was going like this because I really don't like tops like this, y'all. I really don't. Really think the crossback really supports the girls, you know what I'm saying? Because it's crossed. So like it's like, you know, that tug on it. And I don't like wearing bras. And y'all, I don't know why I'm really never comfortable like wearing bralettes like this. But I feel like this flatters my top so nice. I have a man's shoulders. I'm never comfortable wearing tops like this. But I'm really feeling this right now. I'm really feeling this top, this little bralette. I would definitely feel comfortable wearing this out in public, you know? And without feeling insecure. I think this is so bomb. So yeah, make sure y'all get this bralette. And I got this in a medium and this in a medium. But I should have got my leggings in a small. It's still cinches in your waist even regardless. Like, come on. It's giving. Y'all, I don't even want to take this off. Like what? And the material on this feels so good, y'all. Butter or cream or something. Like I just love the material on this. And I really feel like this blush color really complements my skin tone, my tan. Now I want to take this off. I want to keep this on. And just to point this out, y'all know this is a nice, thick material because for one, I have no, um, my boob tape or any nipple cover under over my nipples, y'all. And if y'all have seen it in the beginning of the video, my nipples just be like, bing. Y'all, you can't even tell. That's how good the quality is coming in my outfit online pieces. Okay. So y'all got to pick this up especially. So the next items that I have on girl are from their lingerie collection. Again, I have on the signature boxer shorts. Love these. I love these. Okay. And then I have on this sporty sports bra, which I love too. I really thought I sorted out y'all. I did not think I was going like this back. I like this. This, this top, I swear, like I feel so confident in me. I feel so comfortable. I don't feel insecure about my shoulders or anything like that. I love the swoop neck of the sports bra. Definitely can wear this. Definitely around the house for sure because it's a loungewear. But I definitely feel comfortable wearing it out in public because I really don't mind wearing loungewear out in public, especially if I feel confident in it. So yeah, the back all super sexy bra, the booty. The booty. And like I said, y'all, the fabric, the material, so soft. No bra on. It gives the girl support that it means my boobs are sitting right. No boom tape. No nothing. Like I said, y'all, my outfit online is Miami based. So they, I feel like they already know what the girls want. This is just giving me what it needs to. It's snatching the waist. And these are a medium too. I got a medium in the boxers as well. And I feel like the band on the boxers are a little bit tighter than the leggings because the medium and on the leggings were the band was a little bit more looser. But on the shorts, it's tighter to me. But yeah, on the boxers, it's definitely tighter, just so just the FYI. So I feel like I didn't need to get a small in the boxers. I feel like the medium is a good size for me. But in the leggings, I feel like I needed a small. And then I got a medium in the top as well. Y'all, like I love like both of the outfits so far hate. You is gonna need this. Okay. Okay, Karisha, Karisha, please. Okay girls. So the next outfit I have on is the unforgettable crop top. They're just high, high waisted shorts. Y'all, when I tell you, they literally give you snatched. They give you snatched. Look how thick this band is.  So that's why I am in love with this. I'll say I'm in love with their leggings. I love with their high waisted shorts. Like come on. Everything that I picked out is giving right now. It's giving me life. The material, like I said, y'all so soft. I love this top, this crop top. And it's literally having my girl sitting like, look at my boobs. Look at my boobs. They're sitting up right. No bra, no nothing, no support, just the shirt. This is crazy. This is crazy. Like I feel like I look so good. Look at the body. Look at the body. Stop playing with her. Stop playing with love this outfit. And this is in the color mocha. I love this color on my skin tone. I feel like this will look so good on any skin tone. Honestly, I love me a good brown color. Y'all like, my life just went out. Do a hater. I don't want to take these clothes off. The material is so soft.  This is just so, everything just makes me feel so good and confident. Like I can literally just throw this on and know I'm feeling good. Okay girls, so the next outfit that I paired together was the Kimmy bodysuit with the high waisted leggings. And I was waiting on these leggings, y'all. I was waiting on these because I already have the new pair, y'all. I swear to you, these leggings are literally the best leggings that gives you snatch.  And I really wanted to compare these leggings to my Wolford, the perfect fit leggings. They are very, very popular and they really do snatch you. But y'all, these, these leggings right here, you need these leggings in your closet, period. You're going to want to wear them all the time. These leggings are going to be your go-to leggings, I swear to you. They give you a snatch waist. The booty, the booty. Stop playing. Y'all, y'all see me in the mirror actually. You see, you see how snatch that is back there. Okay. These leggings are $4295, I believe. Those, that price is so affordable, y'all. So affordable compared to Wolford. Wolford, those leggings are like $200 some dollars. And I was a fool for, you know, buying those when I could have just got these at first. And I swear to you, y'all, they really give you the same effect for a more affordable price.  And I cannot wait to start wearing these more often. And then this body suit, y'all, so cute. The cleavage, I love it. It's sitting the girls up right and it has a full zipper so you can literally control how much cleavage you want to show. And this is a good amount, you know?  Don't play with me. Don't play with me. And y'all need to get these leggings, I'm telling you. If you get anything from this video, get a pair of leggings, okay? And you can dress these up or down.  This stuff is so comfortable, y'all. You're not even going to want to take it off.  I can't breathe or nothing like that. I just feel uncomfortable. But y'all, you are not going to want to take these clothes and items off.  So, and I'll be quick to take off clothes, y'all. Okay, girls, so the next outfit, the Kimmy Roffler. And this is in the aqua gray color. This color is so pretty, y'all. It's snatching me in my stomach area. I love that. Making my thighs, my hips look so good. It's, look at, oh my god. And y'all, like I said, the material is one. Like, I feel like I have on some a pajama set on right now. Like, I feel like I can go to sleep in this. That's how soft it is. And the quality is amazing. My nipples don't show. My girls are sitting up again. So, if y'all want to try out anything from my outfit online, get a romper jumpsuit or something in the leggings. I'm telling you. So, get everything if you want. You know, I'm going to find a discount code for y'all so y'all can get whatever you want. Cash out. Okay, y'all. So, the next outfit is this Wildback Romper. And it's basically self-explanatory Wildback, baby. Okay, you see that back there? You see the body in the mirror? I swear, y'all, y'all, like I said, y'all, I really don't like my back out like that. I don't know why I'm weird. Yes, because I have man's shoulders. But girl, this is giving. Okay, period. And this is in a size medium. I really am scared about the top part right here because when I was rolling it over, little nipples were coming out. So, I feel like if you have like bigger breasts, I feel like you should size up because the top part is just, you know, the boobs are just jiggling all over the place. But as far as like on me, like this size, it's a good size. I just can't bend over like that because I feel like it would just, you know, come out because obviously these straps are thin. So, it's not really like, you know, tugging on it really good. But it's giving. It's definitely giving. Don't get me wrong. This is definitely cute.  See, look if I, like now, I can't move too much or my nipples just gonna come out. So, just keep that in mind. But this is definitely very, very cute. The cover is cameo. What the, I love how this looks on me. So, this will be a little romper I would wear if I'm just not doing no hard partying or nothing like that. I'm just sitting around looking cute. So, this would be, you know, that type of romper. But like I said, the top part is just barely no support. But it's giving. Okay. Y'all, I swear I thought I was going like this. I swear. I swear to God. I swear. Oh my God. I probably got to like it. But it's cute. It's cute on a model. But yeah, this is giving. Like I said, the same material, the same quality. So, the straps are just thinner. But it's giving. Ooh, baby, it's giving. Okay, girls. So, the next piece that I got is the Wild Back bodysuit. And I think I like that bodysuit way better than the romper. I don't know why it gives more support. And girl, I just love how basic the front is. Okay, I don't know why I just love this little, like the side. I just think that is so sexy. Like this is in the size of medium. And the tan is just making it look so much better. The tan with the clothes. Geez. Girl, do not put them in this dress. Do not play with me in this dress. Okay. So, literally, when I seen this dress, y'all, I was like, oh my God, this is so perfect for vacation. It's just so simple, but yes, so sexy. And girl, when I tell you this part right here, this part right here is snatching me, okay? This is basically giving me the body that I need, you know what I'm saying? Without my phone. I love the V cut on here.  Y'all, this is giving me everything that I need. Okay. And I just love the favorite part. My favorite part about this dress is definitely like the cinched in waist band right here. And I also got this dress in orange as well because I really couldn't design what color because I really love yellow and orange on me, especially when I'm tan. So, y'all, I just couldn't decide. And I just had to get both. And y'all, when I tell you this dress is giving, okay? It is a little tight right here around my neck, but I feel like if I play with it a little bit, it will just get a little loose with it. It's not irritating my neck. But other than that, I love this dress. I love it, okay? It's giving me everything that I need. Please take me on vacation right now so I can wear it. Okay. Curie. I don't know why it's giving me Marilyn Monroe vibes when she was like, like, I never had a dress like this. So I'm really living, okay? I'm looking for that perfect vacation dinner dress. This, this will be a good choice for sure. And then in this dress, I also feel like my boobs aren't going to go anywhere. I'm going to have a nip slip or anything like that. I feel like my boobs are very, very secure with this band right here. So I really like that. Okay, girls. So this next dress is what I was most excited about, the tube dresses because I just feel like tube dresses are just a simple dress. I love a simple piece where I could just dress it with accessories, compressing my breasts. I was really nervous about that because sometimes, you know, like I said, my shoulders looking crazy. This is really making my chest area look so good and flattering. And I got three colors. I got the long one in black, and then I got the short and white. So, and I'm so excited about these. And like, and this dress is made out of the same material that I've been telling you about. The bomb material is giving, you know, baby steps. It's giving baby steps. Okay?  The body is snatched. This is making my body look so good. And the band is definitely supporting the girls. No nip slip over here. No nip slip. No nip slip. No nip slip. Oh my God, y'all have to get on to my outfit online, y'all. Y'all are not going to be disappointed, okay? Okay, girl, that is it for this video. I hope you guys enjoyed. Let me know which pieces you're gonna cop in the comment section down below because I'm gonna know, girl. And I'm telling you, you need to get the leggings. You need to get the black leggings, any type of leggings, any color.   Nothing. They understood what the world's wanted, okay? So anyways, y'all, that is it. I hope y'all enjoyed. And let me know if y'all like this setup, okay? Because, you know, I'm kind of feeling it.  That is it. And I'll see you on the next video. Bye.


We're back to celebrate global connectivity with Think Tech Global, and we have our bureau in Varanasi, India, in the northeast quadrant of India, and we have our regular reporter, our Karnaki Mishra, who just graduated recently and took his Bachelor in Business Administration. Congratulations, Karnaki. Thank you. So I suppose I should also congratulate Varendra Modi because he won the election, hands down, the international press said that it was a sweeping victory. Can you give us a handle on what happened? Yes. First, I'm going to say that Varendra Modi is an anti-Polish member of parliament from my own city Varanasi. So I can say what I have seen in the last five years, a lot of work has been done from 2014 to 2019, a lot of development is done in my city because we took from my own city. We have been elected from the city of Varanasi, and we won the majority, and far better than last time. We won three-tenths out of five weeks last time, and we won three-fifths victory this time. So we created a massive for Prime Minister Modi. So what were his challenges? I mean, he did have some ups and downs during his administration last time around. I remember, for example, the question of the currency, he wanted to get all the hard currency out of circulation and make it into a more modern financial consumer system. And for a while anyway, it was not all that popular. So what was his level of popularity going into this election? What was his level of popularity going into this election? His popularity definitely increased. I should say, from last five years, whatever work he did, it gave people the confidence that this person is a good leader for the next elections, and the children, again, with a sweeping mandate. So it gave them the majority, and this popularity increased. Those some of the intelligence were criticized, but people overlooked that and voted for another leader. So 900 million voters, was this a question of a simple majority vote? In other words, you don't have an electoral college like we have in the United States. You just count all the votes and decide who had the sufficient votes. And I guess a majority would win, am I right? The U.S. works under presidential system elections. India works on the parliamentary style of elections, similar to the British ones, which we had in the past, a little bit of British legacy in the parliamentary elections. So there is a big difference. We left one person from each seat, and the party having most of the seats became the majority government. So it becomes very difficult to get a majority leader. And there are almost, I think, 5-40 seats in total, and you should get around 172 to get a majority to form a government. What areas of India were his strongest supporters? What part of the political spectrum, you know, gave him this popularity? Was it the big cities? Was it the rural areas? Was it the east, west, north, south? Who were his biggest supporters? Biggest supporters, I think, were the people who wanted to work for the first time, the first time voters, the people who were working and were benefited by the political spectrum. So those schemes were there, gender and movement were there. You can call this banking account for everyone. Free gas connections to people of people. Mobitair was also there, life insurance, or health insurance for people of people. So they had cash benefits from there. So these were all the reasons why he was so popular. Not just in urban cities, but also in rural areas. In rural areas, he promoted people in the rural areas, so that open participation in the campaign. So a lot of efforts were made by him. So the overall development of India takes place, and that's the reason people wanted for him, and what he did wanted for me. And what issues was he campaigning on? Was it the economy? Was it foreign policy? Was it, you know, domestic issues and human rights? What was he strongest on in terms of his platform? I don't know. We basically campaigned on two basic issues, which were his primary updates. His primary is one was when we were in the government, how we increased the growth rate, and second was nationalism. National security was one big reason, and was a very good concern for India. In this year only, in 2019, a terrorist attack took place in Kashmir and killed nearly 40% of our citizens. So now we took decisions to reach Pakistan with him, and he said it was the best in Pakistan should the curve, should the curve go. So again, there's a lot of methods here of doing things like that. But he is fighting for the nationalism, he is fighting for the national building, and he is the country economically also and on the different level of him. We're going to take a short break. This is Karnaki Mishra. We're talking about the election, the sweeping success of Narendra Modi. We'll be right back after this short break, and we'll find out more about what happened in India over the past couple of months in the course of this election. We'll be right back. Aloha. This is Winston Welch. I am your host of Out and About, where every other week, Mondays at 3, we explore a variety of topics in our city, state, nation and world, and events, organizations, the people that fuel them. It's a really interesting show. We welcome you to tune in, and we welcome your suggestions for shows. You got a lot of them out there, and we have an awesome studio here where we can get your ideas out as well. So I look forward to you tuning in every other week where we've got some great guests and great topics. You're going to learn a lot. You're going to come away inspired like I do. So I'll see you every other week here at 3 o'clock on Monday afternoon. Aloha. Hey, Aloha. My name is Andrew Lanning. I'm the host of Security Matters Hawaii, airing every Wednesday here on Think Tech Hawaii, live from the studios. I'll bring you guests. I'll bring you information about the things in security that matter to keeping you safe, your co-workers safe, your family safe, to keep our community safe. We want to teach you about those things in our industry that may be a little outside of your experience. So please join me because security matters. Aloha. Hey, we're back to Think Tech Global. We're talking to Karnaki Mishra, who just recently took his bachelor's in business administration in Varanasi, India, which is in the northeast quadrant of India. And we're talking about the election of Narendra Modi, who won by a sweeping victory only a few days ago in India. So I'm really interested to know how it worked in terms of the involvement of the party.  How well did Modi's party win in that election? I think it was a sweeping majority. Modi won at least 303 seats on his own in the party win 3-0-3-2. And along with the alliance and the coalition which his party had, he won around 365 seats. And he did pretty well in the election. He played pretty well. It was a victory. It was surprising for everyone in the opposition because no one was expecting at least from the opposition that Prime Minister Modi would win in the election again. He played political parties that made the government say that they could defeat Prime Minister Modi by taking part in it. So what do we have going forward here? What does the legislature look like now? What's the composition of it? And I guess this means Prime Minister Modi is very powerful because he's got all these delegates in the legislature, and he will be able to implement his plans with their support. So what will happen in the legislature and what plans will he implement and how does it look for India? Are people encouraged by this election? Do they think that it's going to be a good time? So we won't actually take a majority in this area. So it becomes relatively easy for him to now implement laws or to make laws. And the area in which Prime Minister Modi will work in the future, I'll expect him to work is economic reforms, land reforms and labor laws. I think these are the three primary key areas in which he will be making laws to have industrial manufacturing units in the country and have a lot of money on the government. So is this, would you say that this is a time of progressiveness that the administration now to follow will be progressive under Modi? Is it a time when the people of India will move to a new and better chapter because of this election? No. The first thing about this election was people voted for development. There are not a lot of issues in India if you look at India. Cards are running this tension for India. Even after all of this, people voted for development. If it's just because cars are available they voted for the government which is voting for the development of India. So a lot of good things happened in this election and I hope in the next five minutes many good things happened under the government. One important thing is there that after Prime Minister Modi India Gandhi Modi is the only and the third Prime Minister to secure the majority in a complicated world. So that makes it more historic. So you can see from what Prime Minister Modi is saying this is a rising factor for India and I think national leader of the Indian sector. Now how about the the loyal opposition? That was a party that tried to beat him down and try to win. How well did they do? How well did they do in the campaign? How well did they do in terms of bringing new voters or holding on to old ones? What was their position and where do they sit in the legislature now? Do they have any real leverage in the parliament now? Well, if we talk about democracy, we see after Prime Minister Modi is capable in terms of the national election to join the government. So the opposition didn't see the government as their national side. The new opposition party was the Congress. The Congress Congress and the National Congress and the name of the party. What is the main possibility of the finalist case? And it is another regional party of different areas which collectively tries to do an opposition against the national party. So this came pretty badly in the case of India. They didn't have quality and they didn't have the idea what to do with the elections. So people had no confidence in the Congress party so they didn't see the elections. So we don't have a very strong election in India right now. Now can this go around 40-40? Now it's around 40-40. So you can see there has been much difference in the number of seats and so if you talk in terms of using them so being the leader of the opposition a party must have at least 10% of the population and that's 542 in a year but the leader of the opposition will need 55 seats and this time the people will be the leader of the opposition so they need to form a coalition and be leaders. Opposition doesn't play a role in this. Well I wonder what the world is flat these days we live in a global village and I wonder how much of a role India's foreign policy played in this election what Narendra Modi was saying about the policies that he would follow the policy that he has followed over the past few years and the opposition I mean with China with the United States with the countries to the west and the east how much of a role does that play in Indian politics and in this election? Well the leaders have started with the election of national security all the names foreign policy which we were keeping in mind that Narendra Modi was keeping in mind which was already done from Pakistan which some of us don't know what Pakistan called one major concern for Narendra Modi's foreign policy but how he will tackle these these foreign lands and presently from the issue of the issue of overall development of India with nations like China and the United States I'm hoping that this will go in as a political strategy with the United States and the United States to make a big challenge for Narendra Modi to see how to deal with Donald Trump because Donald Trump sanctioned from Iran and for that moment all is from Iran India is dependent on already from Iran and other nations in the Middle East so this is one big challenge for Narendra Modi to see how he will deal with the Iran crisis right now Donald Trump is there concern in India about American military maneuvers in and around Iran and the Gulf is this a threat or at least a point of concern for the people in India and for the government in India Yes, that's a concern because Iran is the major close ally of India and Iran exports oil and India is dependent on the United States they are cheap and reliable so this is often the expansion for Iran and the expansion is going between Iran and the United States it will be a challenge for the Narendra Modi how to deal with the crisis because we have to deal with the President Trump and we have to deal with Iran and how we can balance between these two powers and deal with the Narendra Modi Well, you and I have talked a number of times and I remember on one occasion when we talked I asked you how you felt about Donald Trump this is about a year or two ago and you indicated that there was a positive aspect to Trump in the sense that he was a strong leader and in these days the world needs strong leaders how do you feel about him now how you've watched him how everybody in the world has watched him for the past couple of years India has watched him with particular attention how do you feel he's doing how do you feel he's doing on foreign policy and for that matter domestic policy Donald Trump I think the biggest problem is the foreign policy of all the Narendra's other nations if you like Donald Trump in the United States he is taking decision for betterment of the United States but he is challenging the allies if you look at Donald Trump and the allies of the United States whether it be Germany whether it be China whether it be Japan these nations are concerned about Donald Trump's foreign policy because it's not that stable he changes the narrative he changes the perspective look for something that's not Korea's summit he has seen success and he's seen young ones and I think that's pretty great but now it's even time I mean not only in the United States but also in the United States the way it is going on so I think the foreign policy is one key area in which Donald Trump has to live I'm definitely feeling that would you be looking forward to the next American president to normalize things to sort of let them settle down so there isn't so much tension in your part of the world would that be something that the average Indian would like to see a president that is more moderate yes I think I would like to see a moderate president in the United States the United States the United States I think that we signed up to be president again many new states are going to be there from Hawaii I think I think one thing that is from Hawaii is that it's going to be for the US election so there isn't so much that's going to be there I think that that's going to be there for the United States and for the world one other thing I wanted to ask you about is you know so now you're a graduate in business administration what is your expectation for the economy of India all these things considered the election international affairs that affect you you know in the way India is working these days do you think the economy of India is worth betting on do you think the economy of India will improve or is it under stress in some way I would say there is a big stress on the economy right now many factors are there I think I think lack of jobs are there so job creation is going to be a big challenge for everyone for the future and infrastructure and various other aspects of the economy I think the economy of India I think that it's going to be better from this time I believe the economy of India will improve but challenges are there challenges are there for everyone Fardaki now you're a graduate and you're a business graduate as far as I can see you've had a very robust education what are you going to do are you going to go to further graduate school are you going into the economy yourself what are you doing these days and what's your plan I'm planning to do an MBA I'll complete my MBA I'm planning to do an MBA from any college or whatever and I want to specialize in particular areas then work in the corporate sector or most of the job so my plan is go for the market will you come to the United States hopefully if I get a chance I will why do I think that you ultimately will and the last question I put to you is you know you're very familiar and articulate about Indian politics and for that matter Indian business affairs and I wonder if there's a place for you in Indian politics I wonder if you would ever consider and whether the community would ever consider having you as an elected representative to the parliament or otherwise what do you think I think politics is a very big field in India if you are educated and if you are with me you can be a good politician I don't think I have a political background right now but in future if I get a chance I will get into politics if I get a chance I will definitely I will and I think the constructive politics for the DCP president of this world I feel that I think you must take part in politics and actively participate in politics so that people increase the number of candidates for the DCP and help the people and when we say there is corruption if we participate then only we can relieve the corruption of these problems of politics if we take politics we will try to be part of politics you know it's really a treat to talk to you Karnaki it's a treat to get your perspective from so far away it helps us understand what we see from here and I hope we can talk to you again in the near term and check up and see how Narendra Modi is doing how you are doing and how India is doing vis-a-vis all those countries around you it's very exciting to be able to talk to you and I look forward to our next discussion thank you so much Karnaki Mishra India, enjoy so much talking Aloha


We have tried to do, trying to do interacting systems where molecules interact with each other and we have done Meier's theory and Meier's theory which is we have rise to many other theories but that is essentially theory of real gases and compensation. One thing I forgot to tell is that this is also called, we did the reason of that that it breaks down at high density but it is more famous in physics, this subject is approached by famous surfaces in a very different way, this is called high temperature expansion. The reason is high temperature expansion if you look at it that the Meier function F which is e to the power minus beta u r minus 1. So when more temperature becomes large beta becomes small so F becomes small so these kind of grams that becomes less important than these and then these become less important than these. So at low density of gases anyway this will be favored over these because they are not many molecules volume is volume and these will be more favored than that, draw a little bit larger which will be picked up through the when you calculate the partition function the cluster integrals and irreducible cluster integrals but equally rigorous way of saying that the Meier's theory essentially and high temperature expansion and Virial series is a series in density but it can also be considered as high temperature because the higher Virial coefficients rapidly decrease with temperature. So that is a different view which comes from e to the power beta u and this high temperature expansion perfects all through statistical mechanics simply because of the Benjamin factor e to the power minus beta. So the difficulty comes in statistical mechanics because of the interaction between particles and we cannot evaluate the partition function we cannot evaluate the total number of microscopic states and that is why this few cases we can do rigorously plays a very very important role because they guide us and they provide us insight. Just like Meier's theory went on to tell us what is a Virial series and went on to develop many other things like I told you Soljale transition, percolation, the cluster in phenomena, the cooperativity which is really I explained is a beautiful phenomena that you can have 10 intermediate size clusters say in a particular you can have a particle of 100 you can have 50 monomers and dimers but other 50 particles can be distributed among the clusters which are 5 of say 10 particles. Now when you increase one or two more particles these large particles can get connected because another particle can come in between. You can imagine it easily in a lattice in a cell that there are these clusters which are connected lattice size another big lattice size and then there is an empty between them but as we increase the probability or the density probability of finding a particle which is same as density then that can get connected. So what happened in a very infinitesimal change this 5, 10 m can become 150 m and suddenly this intermediate size clusters disappear from the system and that is what happens when the range see after range the clouds all the things comes down and sky become clear and you do not see any any any any a humidity beyond the point goes down and everything at least upper atmosphere. So this is the same thing the cooperative so that in that sense Bayer's theory is a great theory and give lot of things but it also has its limitations as I said that it cannot be pushed beyond the point where everything diverges and I cannot extend to low temperature and high density but with that cabinet we will go ahead and do the next thing. So second interacting system which of great use in statistical mechanics and find great use in phase transition and because it is solvable in certain exact in certain limits it can be solved exactly it plays perhaps the most important system in the entire physics of interactive physics and chemistry of interacting systems and this is the ising model. Ising model is a simple one dimensional ising model is also same thing is available for or three dimensional but they are equal to dimensional 2D ising 3D ising but the original ising is 1D and then this is essentially you have a condensational chain or rod and you have the spins we just spin so you can take them dipoles whatever and they are interactively with each other so they can be parallel anti-parallel all possible so the spins can be so definition of ising model is that it consists of spins spins can take only two directions. So let me write down the assumptions of the model spins can be can be only up and down and they are denoted by plus 1 and minus 1 as if one is the plus 1 and minus comes to a great extent from the logic that you have an external magnetic field these are only for magnetic systems you have an external also it goes over for electrical systems we use that in real dipoles. So now the spins can be up and down and they are done denoted by plus and 1 and the variable that comes is sigma i and sigma i can be plus 1 and minus 1 if it is plus 1 is up and minus 1 is down and what a stop telling in a minute ago that why this is chosen essentially because you have a field in mind and cos theta and so up is the field is aligned on the top that is just a moment lecture you can do it any direction you want but up and down cannot change in ising model so it is cos theta and cos pi so plus 1 and minus 1 that is the logic of these two things then number 3 an important very very important thing that I have only nearest neighbor interaction only nearest neighbor interaction that means these spin here can interact only with this one and that one. So in a finite spin when we want to finite change we do not want to do in order to reduce the effect of the boundary we impose what is called a periodic boundary condition that means we form a ring so after that it becomes this one this periodic boundary condition which is used in many many areas of the schematic computer simulations that not a part of the assumption the part of the assumption of these three the spins can be only up and down and so you do by plus and minus 1 and the only nearest neighbor interaction is taking it out so given that you would imagine that is a trivial thing to solve but it turned out no it is highly non-trivial nobody has been able to solve three-dimensionalizing model they are at one time they are a sporadic claim so three-dimensionalizing model but has not been able to do nobody the previous people have tried nobody has been able to do and the two-dimensionalizing is extremely difficult and still called the most difficult calculation in the history of physics and that was done by Lars von Sager so the physical chemist very interesting now so we go now write down an Hamiltonian what called Ising Hamiltonian that we wrote down the other the H equal to okay let me write down the A1 then I general one so the I know spend some time on this so this is is a generalized version of Ising model where the interaction depends on the location that means this interaction can be different from this interaction so if I call that one two three four five six then one two can be different from two three and this plays a very important role later but not we don't need it now so we consider them to be constant and take it out so J okay so this done such that when these are both up or both down then I get plus for both of them and then it becomes minus and that is favored and that is called ferromagnetic interaction when parallel spins are favored similarly negative one but however is a plus and minus like in this case or in this case you have one plus one minus so that becomes minus one and this becomes plus so that is not done and now this is the magnetic field so magnetic field now if I again a matter of convention these are all matter of convention but they are perfectly generally you can change convention if you don't like this convention this also will not change so this is the magnetic field that is acting on it which absorbs in it to combine the dipole moment or magnetic moment of this beam and the external electric field that means a magnetic field is H and then magnetic moment is mu then B is H mu so that is combined in that the effect of the external field is important of course you can have statistical mechanics in the absence of the external field also which will do but this is the major thing to know and this is the ising Hamiltonian this is a general Hamiltonian valid for any dimension you can have two dimension you can again have spin up and down exactly same thing n square lattice the number of nearest neighbor here is 2 it becomes 12 if you go to triangular lattice then number of nearest neighbor becomes 6 then you can go to FCC or BCC lattices and which are just a historical comment that when you go to three dimension you cannot solve it radically and you do fall back on a high temperature expansion which is very similar to me yes it is really interesting and huge number of people building 60s and 70s used to do these high temperature expansions of the three dimensional spin very very famous scientist don't worry okay so we have now defined the ising Hamiltonian and now I spent a little time telling you why such a simple Hamiltonian it might not look so simple to you because if you are not used to kind of abstract things this is sum over i and this is sum over given one configuration this is so I have 1 2 1 3 2 3 2 just like we did okay so this ising Hamiltonian I will now spend a little time before I go to calculations to tell you what are the basic merits and certain things of this you know what I have in notes is much better than written but it is better than that but let's see this will do little bit of the work that I intend to do there too much too much needed here okay so these are lattice models so some of them are radical solution as possible okay so this is the spin that I am talking h n of n spins and this is the Hamiltonian the ising Hamiltonian and this is the you can understand now what is important thing to realize that very important to realize there are n spins now at any given instant or any given configuration these spins are all having configuration which could be which is different from another configuration but each configuration comes with an energy so a given configuration this Hamiltonian is for a given configuration okay for example let me consider this one I will pick up a minus from here let's see my integral is 0 I don't need it now I would not need it for some time now now I will pick up a positive contribution from here another positive another for some reason everything positive here the person would do it is all anti-parametric kind of interaction okay but if it were up then as I said so a given configuration a given configuration comes with a given energy which is exactly same we have in gas phase that where at any given configuration a number of particles are interacting with each other and that configuration has an energy and Boltzmann told us taught us that the weight of that configuration will be given by the energy of that configuration and this is very essence of the statistical mechanics how we built the thinking in statistical mechanics okay so again the Hamiltonian given here one says what is ferromagnetic or the anti-ferromagnetic all these things okay now how do you do the partition function now in partition function these Hamiltonian has to go in the numerator of the exponential right minus this there in front of minus beta H that minus takes care of the minus and minus here I get positive now the difference between the my earlier thing is that I have to add over all the configurations so before so the sum over spins goes here in the exponential but this is weight of a given configuration but I have to sum over all possible configurations so this is the same as in my classical or continuum statistical mechanics the integrations over positions is the same as the sum over spins there I take a configuration particles are in the position R 1, R 2, R 3, R 4, R n and then I get an Hamiltonian for that then what I do I integrate over all possible positions of the first particle second particle third particle d R 1, d R 2, d R n which is exactly same thing we are doing here we are taking over all sum over all possible spins but now you understand that it creates enormous number of configurations because these spins though only can be up and down it is a if n number of spins are there they are 2 to the power n and if n is large number like abogato number then you have a huge number of configurations there so the entropic part enters through all possible combinations and they are into a okay so now the partition function is this thing this we need not worry right now okay so okay now I want to there are going back so the isic models are explains for what is of is particularly for isic models solids polymers micelles reverse micelles this simple thing is used rather extensively and also the isic model that we do is used for gas liquid transition even condensation you can have a nearest theory version of the isic model or isic model version of the isic theory and this is the one was part of the thesis okay now what I am going to do I am not going to do this difficult thing I will do something little simple and because it will become it could become very difficult and I think I have explained that this particular spin comes with an energy that energy goes to Boltzmann factor in exponential and that gives the contribution to partition function of this particular configuration this is not good I think that is the one we discarded right yeah now I am going to consider only this part I am neglecting for simplicity now because I will be able to do something now delete it so I now have a partition function n is a function of p n number of spins at temperature 3 sigma 1 sigma 2 sigma 3 sigma n for the spins then 2 to the power minus beta j sigma 1 sigma 2 so this is the partition function I need to evaluate with the condition that sigma 1 sigma 2 are they can take up and down should be plus where plus beta so now you notice the one thing that all these are coming as product so I can introduce a composite variable sigma j c equal to sigma j minus 1 sigma now let me see what are these composite variables will take now composite variables will be when this is plus this is plus then minus minus again plus it is a plus minus minus so composite variable while each of them have two variables composite variable has four variables okay so these quantity now I can now write in terms of composite variables which is now I can now I can now calculate these contribution of these of course I have to do when j greater than equal to 2 because I have 1 2 2 3 like that so j goes from 2 so in this case j has to go from 2 to particle okay now I have to do this composite variable so now I write this as bring I bring the product outside and I take the sum inside this is my composite variable now sigma j c okay then e to the power beta j sigma j c all right now I can take each 1 j and let me calculate the composite variable so now that will be e to the power beta j sigma composite variable c and sum over say j j speed then sigma j c has four values so that will be e to the power plus beta j plus minus minus e to the power minus beta j I have plus minus e to the power minus minus plus plus both minus then I have plus minus and minus plus so that would now be 2 into e to the power beta j beginning to take the character of insulator ising model so this is a what I have done actually is equivalent to a factorization I have factorized I could factorize because of this this form of what I deleted the form of that thing so I have done a factorization just the factorization I do but that factorization suddenly gave me a wonderful form which now does not depend on j just the beauty then what I can do now I can make this product here so now I can replace now these by so many times the product n minus 1 but n is very large so I do not really care of that so I have evaluated the partition function in the absence of a field of the ising model let me do some work with that the way I always did was like this this way I always decompose factorize that is the way I learned but in the book that we have written is not like that and that is the say like now we have to really correct because this is the way one should go but most of the books jump into probably Carson Wang has this way of doing things because I remember that this is in many places the composite variable but I am unfortunately most of the places I looked into the start with the very complicated transfer matrix all these things which is at least for it can ask for this concept and now people is not a waste way to start these things okay now there is some extremely important thing coming out from there now that is then I am just neglecting n is very large so I am putting that equal to n I hope I am doing all this right now what is this quantity e to the power beta j plus e to the minus beta j so now again 2 to the power n so then KBG are area so this term I can want to write take it out so plus this second so these two cancels right these two cancels so I am left with partition function now so in the absence of a magnetic field I have obtained the free energy I am obtained the partition function of the free energy now there is something very important here you know this continues to be in the principle magnetic field the important part here is that these there are certain functions in mathematics which are called entire functions exponential is an entire function cause is an entire function and what is an entire function that has infinite number of derivatives and is continuous all through that function is called an entire function so these cause is an entire function so it cannot show any discontinuity if it does not show any discontinuity it cannot show any phase transition and these one of the primary result of the theory of phase transition is that you cannot have a phase transition in one dimension so this is also called a beautiful theorem Ascot-Merbin theorem but we no need to go into Ascot-Merbin theorem at all at least not in this kind of rather preliminary things that we are doing but it is important to know that these cannot show any singularity so it cannot describe phase transition I can calculate entropy I can get a DA dt of that and get the entropy right and get the specific heat and then I can calculate the fluctuation in energy specific heat and then I can find those two are the same all these things one can do and people have done because this is the one model which has been bitten to death but important result here is that because of these kind of beautiful expression nice neat analytical expression that we do have a completely analytical function so there was this this gave rise to a lot of logic a lot of logic and a lot of controversy that a little bit of history that why the how statistical mechanics can at all describe phase transition that means since Boltzmann is exponential and exponential is an entire function differentiable completely to all order how come then a statistical mechanics which is in the form of the sum of the exponentials as we have seen here sum of the exponentials can give rise to a singularity that was a huge debate in you know for more than 2-3 decades which was ultimately solved in a specific case by Onsager but in a very general case a beautiful by CN Young at DD Lee called Young Lee theory Lee theory two very famous physicists who also did quark and parity violation and they went on to get the Nobel Prize for that but there another beautiful work was showing how and we use the Ising model and use the mayors theory actually more mayors theory than Ising model to show that how singularity can evolve by doing a beautiful piece of complex analysis that we can do sometime okay so this is with the in the absence of a magnetic field in the presence of a magnetic field is a little bit difficult so I will not do it in the class but I will go through that little bit and then I will give you the final result is not too important that we do it for the major way course of the thing those of you are interested you can do it and if you get stuck you can come to me and I will do it.