Statistical Theory for Displacement Ferroelectrics. II. Specific-Heat and Soft-Mode-Frequency Calculations

The effective field theory for displacement ferroelectrics which was developed in part I of the present series of papers is extended to include specific-heat, energy-of-ordering, and more detailed soft-mode-frequency calculations. Numerical results are computed for a simple one-soft-mode system in preparation for a test of the theory on the displacement ferroelectric LiTa${\mathrm{O}}_3$ (which is presented in the following paper). Detailed shapes of the specific-heat curves are computed and the discontinuity at the Curie temperature is displayed. The soft-mode-frequency calculations are extended beyond the small-anharmonicity region discussed in part I, thereby removing the last small-anharmonicity restriction from the method. Freed from all small-anharmonicity restrictions, it is demonstrated that the present approach is no longer confined to displacement systems, but is equally applicable for order-disorder ferroelectrics and goes over quite smoothly from one class of ferroelectric to the other.