Phenomenological approach to the description of phase transitions in solids

A general model approach to the problem of describing the competition and coexistence of different phases of a condensed state is considered on the basis of Landau's theory of second-order phase transitions. We show that the multicomponent order parameter leads to a more complex pattern of phase transitions and the appearance of regions in the phase diagram in which different spatially ordered states can compete or coexist. The solution of the necessary equations of the Ginzburg-Landau theory was carried out by the variational method. The model considered in this paper is applicable to the analysis of phase transitions in solids with different electrical properties (transitions to the superconducting state, metal-dielectric and metal-semiconductor transformations) and magnetic states (paramagnet-ferromagnet, paramagnet-antiferromagnet). The proposed approach makes it possible to numerically simulate the free energy of a solid near the phase transition points. The necessary conditions and limits of applicability of the analyzed computational model are indicated.