Phase Transitions - 1: Methods of Convex Analysis

Abstract

Ever since the problem of phase transition had been posed, around 1925, an extraordinary number of methods have been developed in order to solve it. We shall describe briefly in chapter 8 certain methods that have played an important historical role, in particular, Onsager’s method (section 207). Apart from those, the other methods that have so far produced the most interesting results may be associated with three lines of thought:

• methods that have resulted from refinements of Peierls’s idea (section 9), which we shall discuss in chapter 6

• methods based on “positive reflexivity”,developed by Fröhlich among others, which we shall discuss in chapter 7

• methods based upon a certain number of inequalities, which we shall discuss here