A classification of phase diagrams by means of “Elementary” Catastrophe Theory (ECT) II

Abstract

In a previous paper it has been shown that near every type of point μ o in the field space, any GM stable C∞ unfolding Φ by appropriate diffeomorphic substitutions can be reduced to a GM standard form, i.e. an unfolding of functions, constructed from one or more simple polynomials. For μ o being a critical point the result of the reduction is compared with the Landau theory. This is followed by a complete list, up to and including four fields, of phase diagrams, described by GM standard forms, with physical examples (including e.g. critical end points and tricritical points). Symmetries are also treated. Finally remarks are made on, among other things, the “double cusp” GM standard form and a one-to-one correspondence between types of points and QLS of PS, described by GM stable Φ's, around these points.