Constructing and Classifying Phenomenological Models of Phase Transitions by Means of Catastrophe Theory

Phenomenological models of phase transitions for two- and three-component order parameters are constructed by means of catastrophe theory using equivariant vector fields that consider the symmetry of the thermodynamic system. The models are classified according to the number of control parameters, depending on external thermodynamic conditions. Phase diagrams of some models are constructed and theoretical temperature dependences of their thermal properties are calculated. A comparison of theoretical and experimental data show a satisfactory match in quality.