Structural Phase Transitions in the Single-Ion Model

We have so far used an approach which is usually referred to as the phenomenological theory of phase transitions. Recall that within the framework of this theory we proceeded from the presence of a phase transition and used at the outset only the assumption of a regular, nonsingular temperature dependence of the coefficients contained in the theory (Landau coefficients of the thermodynamic potential). We also found that this assumption is invalid, unsubstantiated, but this was also done within the scope of the phenomenological theory. In this theory we were not interested, as a matter of fact, in the concrete structure, the chemical composition of a crystal, and the character of forces that are operating between particles (examples given in Chap. 1 were aimed at rendering the treatment more spectacular, but they were not required for constructing the theory). The only essential point that we took into account was the character of variation of the crystal symmetry at the Curie point. Therefore, we could say nothing of the values of the coefficients included in the theory and interpret the nature of the interactions leading to a phase transition.