The Construction of Phenomenological Models of Phase Transitions Using Equivariant Catastrophe Theory Methods

A method for the construction of phenomenological models of phase transitions using the equivariant theory of singularities of differentiable maps with the symmetry of the order parameter (the equivariant catastrophe theory) is considered. This method differs from the traditional series expansion in powers of the order parameter in that, firstly, there is no requirement that the order parameters be small, and only the number of thermodynamic parameters that are varied in the experiment (temperature, pressure, etc.) is given; secondly, derived models have structural stability for an adequate description of the anomalies of the physical properties near the phase transitions. As an example to illustrate the method, a model of phase transitions with a two-component order parameter is constructed.