MEAN-FIELD THEORY OF ENTROPY-DRIVEN STRUCTURAL PHASE-TRANSITIONS

Models for lattice dynamical systems possessing first-order structural phase transitions have recently been constructed, and extensive molecular-dynamics calculations have been carried out for them. The mechanism producing the transition is that there are lower vibrational frequencies in the high-temperature structure than in the low-temperature structure, thereby increasing the entropy of the high-temperature phase. These structure-dependent frequencies are produced by anharmonicity in the interparticle interaction. This paper describes a mean-field theory for such entropy-driven transitions. It is based on making a Gaussian ansatz for the single-particle probability density function. Qualitatively, the results agree well with the molecular-dynamics simulations. We use the theory to make a more extensive survey of the parameter space than has been done with the simulations. We find that there are three different intervals for the strength of the anharmonicity, in each of which the high-temperature behavior of the order parameter is different in an important way. This change is a possible explanation for the hysteresis found in the simulations.