Classification of the Phenomenological Models of Phase Transitions with Two Interacting Order Parameters Using the Catastrophe Theory: L = C2v

Abstract

The phenomenological models of phase transitions for two one-component interacting order parameters have been classified using the methods of the equivariant catastrophe theory. The models have been constructed based on the number of control parameters, which depend on the thermodynamic parameters varied in experiments (temperature, pressure, chemical potentials of impurities, etc.), rather than by simple expansion of the thermodynamic potential in series of order-parameter powers. The models with the order-parameter symmetry group L = C_2v are classified in terms of the number of control parameters from two to five. An infinite series of the phenomenological models with biquadratic interaction of the order parameters was also obtained.