States of equilibrium of condensed matter within Ginzburg–Landau Ψ4-model

The states of equilibrium of condensed system are considered within the framework of Ginzburg–Landau Ψ4-model. The three types of solutions, which describe the spectrum of equilibrium states, are obtained for the case of periodic boundary conditions. The one-parameter family of a stable, in the sense of Lyapunov solutions is referred to the states of equilibrium of the first type, while to the second and the third types are referred the states corresponding to two-parameter families of unstable solutions. It is shown that at critical values of control parameter the inverse bifurcation of unstable solutions of the second type from that of the first type takes place. The states of equilibrium of a condensed system corresponding to these solutions prove to be degenerated with respect to energy, i.e., transition from nth unstable state in the nth stable state occurs without heat effect. For transition between the stable states of equilibrium (solution of the first type) the formulas for calculation of thermal effect are obtained. Solutions of the third type retrieved in the class of elliptic functions describe the states with energies higher than energies of the relevant states of the first two types. The restrictions imposed by two-parameter families of unstable solutions on the states of equilibrium in condensed systems are considered.