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

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.