A Catastrophe-Theoretic Approach to Tricritical Points with Application to Liquid Crystals

TL;DR

This paper introduces a criterion based on Elementary Catastrophe Theory for identifying tricritical points in phase diagrams, applicable to systems with complex free energy landscapes and multiple order parameters, with an application to liquid crystals.

Contribution

It develops a unified criterion for locating tricritical points using Catastrophe Theory, extending previous methods to non-symmetric free energies with multiple order parameters.

Findings

Criterion applies to non-symmetric free energies

Tricritical points occur when free energy is not 4-determined

Application demonstrated on smectic-C liquid crystals

Abstract

A criterion to locate tricritical points in phase diagrams is proposed. The criterion is formulated in the framework of the Elementary Catastrophe Theory and encompasses all the existing criteria in that it applies to systems described by a generally non symmetric free energy which can depend on one or more order parameters. We show that a tricritical point is given whenever the free energy is not 4-determined. An application to smectic-C liquid crystals is briefly discussed.