Analysis of a three-component model phase diagram by Catastrophe Theory

TL;DR

This paper applies Catastrophe Theory to analyze the phase diagram of a three-component lattice gas model, identifying key singularities and establishing a canonical form for understanding its thermodynamic behavior.

Contribution

It introduces a novel application of Catastrophe Theory to a three-component lattice gas model, revealing the structure of its phase diagram and singularities.

Findings

Identified the highest singularity with codimension five.

Established transversality of the singularity.

Used the $A_6$ Landau potential as a canonical form for analysis.

Abstract

We analyze the thermodynamical potential of a lattice gas model with three components and five parameters using the methods of Catastrophe Theory. We find the highest singularity, which has codimension five, and establish its transversality. Hence the corresponding seven-degree Landau potential, the canonical form Wigwam or $A_6$, constitutes the adequate starting point to study the overall phase diagram of this model.