On the second-order phase transition initiated by a strong electron-phonon interaction

A model of a crystal with a strong electron-phonon interaction that initiates a second-order phase transition has been considered. The purpose of the study is to determine the temperature dependence of the thermodynamic potential of the symmetric phase in the temperature range in the immediate vicinity of the transition temperature TC for this model. The problem has been solved using the quantum Matsubara Green’s function approach, which takes into account the influence of both thermal and quantum fluctuations. It has been demonstrated that fluctuation coherent deformations of the crystal lattice with the same symmetry as in the ordered phase appear to be energetically favorable at T > TC due to the interaction with the electronic subsystem. The results obtained have made it possible to construct the model of the second-order phase transition near the Curie point TC.