If these phenomena occur with a homogeneous singularity in the free energy, then there exist a set of hyperscaling relations among the parameters that govern them.
If these phenomena occur with a homogeneous singularity in the free energy, then there exist a set of hyperscaling relations among the parameters that govern them. These phenomena are accompanied by a divergence of the correlation length, and they can be located by finding the saddle point of the effective field Hamiltonian. Marian Smoluchowski described large-scale fluctuations known as critical opalescence that accompany them. One of them is governed by a parameter beta that equals 1/2 according to classical theory; that one is observed in the (*) Ising model in more than one dimension. The principle of universality asserts that certain classes of these phenomena are all governed by a single set of critical exponents. If the order parameter is continuous through one of them, it is second-order, and may be described by Landau theory. For 10 points, identify these events in which one state of matter changes into another.
If these phenomena occur with a homogeneous singularity in the free energy, then there exist a set of hyperscaling relations among the parameters that govern them.
phase transitions [prompt on critical points]