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We consider phase transitions in crystals with a strong interband electron-phonon interaction. We investigate the thermodynamic potential of the system using the method of temperature Green's functions, which takes quantum and thermal fluctuations into account. We show that in the absence of striction, these phase transitions are realized as a sequence of second-order phase transitions in each of which the thermodynamic potential has a logarithmic singularity, as in the Onsager model. This suggests that this singularity is characteristic of all second-order phase transitions. We show that the energy preference of the transition to the ordered phase is ensured by the electron coupling to coherent displacements of ions along normal coordinates of the phonon modes. We calculate the limit value of the energy decrease in the ordered phase compared with the symmetric phase as T → 0 K. 1.In numerous theoretical and experimental works investigating second-order phase transitions, the thermodynamic potential is used in the form of a regular expansion in the order parameter(s), as first proposed by Landau. The Landau expansion in the order parameters is used especially extensively in the theory of segnetoelectric second-order transitions [1], where the order parameter is usually given by the crystal polarization. In the case of improper segnetoelectrics [2], the order parameters in the Landau expansion are given by certain structure characteristics. But it is emphasized many times in the course of theoretical physics [3] that the second-order phase transition point must be a singular point of the thermodynamic potential near which the regular expansion is inapplicable. The applicability limits of the Landau theory were established by Ginzburg in [4], where he actually proved that the Landau expansion can be applied in the entire temperature range except a very narrow interval that is insignificant in solving practical problems. For this reason, solving the problem of determining the nature of the singularity of the thermodynamic potential at the second-order phase transition point has long been reduced to analyzing the well-known Ising model [5].An essential advance in understanding the nature of this singularity was related to the theory of critical indices [6], but the degree to which the relations between them are exact does not allow differentiating between the tendency of thermodynamic variables to a constant limit at the transition point and their logarithmic increase. Such a singularity of the thermodynamic potential is given by the only known exact solution of the second-order phase transition problem in the Ising model on a two-dimensional dipole lattice [5]. In what follows, we show that the thermodynamic potential for second-order phase transitions due to a strong interband electron-phonon coupling in crystals also diverges logarithmically. An important role of this coupling in compounds exhibiting a displacement-type phase transition was confirmed in [7].

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