Phenomenological Models of Phase Transitions with Multicomponent Interacting Order Parameters: Construction and Classification by Methods of Singularity Theory

Phenomenological models of phase transitions for two interacting order parameters, one-component and two-component, are constructed. The construction was carried out based on the number of control parameters depending on external thermodynamic conditions by methods of the equivariant catastrophe theory (singularity theory), taking into account the symmetry of the order parameters. The classification of phenomenological models according to the number of control parameters is carried out. Phase diagrams of the models are constructed and the theoretical temperature dependence of the heat capacity is calculated, which shows a satisfactory qualitative correspondence with the experimental dependence in the \(\textrm{Rb}_{2}\textrm{KInF}_{6}\) elpasolite crystal.