Basic Features of Critical Points

There is a strong analogy between the statistics of linear, flexible polymers and various features of critical phenomena. To make it clear, we flrst describe some essential aspects of ferromagnetic transition points— fenomagnets are the best example for our purpose. For a more detailed introduction, the classic reference is the book of H. E. Stanley.  

Comparing this with eq. (X.l), we notice a correspondence between N and . To reach a high degree of universality, we want e- 0or N - oo. This correspondence can be cast in a precise theorem (discussed Mow). 

Let us first consider the high temperature side of the transition and determine the main effects that indicate the onset of ferromagnetic order. A first method applies a small magnetic field H to the system and measures the average magnetization M induced by H. For small H this must be of the form M = where is called the susceptibility (not to be confused with the Floiy interaction parameter), xu depends on tenverature and diverges when = (t - Tc)/r becomes veiy small  

A second, more local method of probing was mentioned above—i.e., neutron scattering—which is sensitive to the size of the correlated regions, described by the exponent v [eq. (X.l)]. 

A third approach is based on the specific heat C. In some fe magnets one finds a singularity in C (the specific heat in zero field) which can be represented as 

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