Analysis of a three-component model phase diagram by Catastrophe Theory: Potentials with two Order Parameters

TL;DR

This paper classifies the singularities of a three-component lattice gas model's Gibbs potential using Catastrophe Theory, identifying key canonical forms related to well-known catastrophes and completing prior analyses.

Contribution

It applies Catastrophe Theory to classify singularities in a three-component lattice gas model with two order parameters, identifying specific canonical forms and completing previous work.

Findings

Identification of Landau potentials with two variables

Explicit demonstration of transversality for each case

Completion of the Catastrophe Theory analysis for the model

Abstract

In this work we classify the singularities obtained from the Gibbs potential of a lattice gas model with three components, two order parameters and five control parameters applying the general theorems provided by Catastrophe Theory. In particular, we clearly establish the existence of Landau potentials in two variables or, in other words, corank 2 canonical forms that are associated to the hyperbolic umbilic, D_{+4}, its dual the elliptic umbilic, D_{-4}, and the parabolic umbilic, D_5, catastrophes. The transversality of the potential with two order parameters is explicitely shown for each case. Thus we complete the Catastrophe Theory analysis of the three-component lattice model, initiated in a previous paper.