Method of self-consistent phonon field in the theory of structural transitions

The method of the self-consistent phonon field provides the basis for a general discussion of lattice dynamics in a structural transition, in particular, the criterion for the appearance of a soft mode and the connection between the dynamical and thermodynamical conditions for the transition temperature. The first and second orders in the method of the selfconsistent phonon field are considered, and the role of fluctuations of the order parameter is elucidated.