Self-consistent mean-field theory of asymmetric first-order structural phase transitions

The paper presents a self-consistent mean-field theory for a lattice-dynamical model that exhibits a first-order structural phase transition. In this model the phase transition is produced because the high-energy structure has lower vibrational frequencies than those of the low-energy structure. This mechanism produces higher entropy in the higher-energy structure and thereby drives a phase transition. These structure-dependent frequencies are produced by anharmonicity in the interparticle interaction. The approximate theory of the transition given here reduces the exact coupled equations of motion to a single mean-field equation by replacing coupling terms between neighbors with appropriate averages. This step produces an effective potential that is used to calculate self-consistently the averages that appear in it. Thermodynamic properties calculated by this method show that the system has a first-order phase transition for sufficiently large strength of the interparticle anharmonicity. Further properties of the system obtained by this method include a discontinuous change in the shape of the average displacement and free-energy vs temperature relations as a function of the anharmonicity strength. This feature may be related to the hysteresis seen in previously performed computer simulations on the model. The effective potential also determines the displacement probability distribution function. For the parameter values studied here this distribution has a single maximum with only small asymmetry about this maximum. {copyright} {ital 1996 The American Physical Society.}