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We have constructed a fully-specified model of a diatomic crystal showing a soft-mode phase transition, loosely patterned on tin telluride. The model can be used to test the accuracy of different techniques for studying the phase transition. Here we apply the self-consistent phonon theory (SCI). Using this theory, we do find a soft mode in the high-temperature, cubic phase, and the free energy shows the Landau form, consistent with a mean-field theory of a second-order phase transition. However, the frequency of the soft mode calculated in the self-consistency iterations does not go to zero at the phase transition. It is pointed out that, even within the SC1 approximation, the frequencies associated with the response functions of the crystal should include additional contributions, corresponding to cubic and bubble-diagram shifts. With these contributions included, the frequency does go to zero at the transition. The shape of the spectral function is also discussed.

The application of molecular field models to the calculation of the thermal properties of ferroelectric crystals is discussed, with particular emphasis on the sequence of phase transitions occurring in barium titanate. The parameters of the model are related to first-principles energy calculations on the one hand, and to the Landau-Devonshire thermodynamic method on the other. The necessary conditions for the model to display a first-order transition to the disordered, cubic, phase are discussed. Results are presented for one- and three-dimensional models which show most of the features displayed by barium titanate.

We use a moment-expansion method for the spectral functions to show that a one-dimensional molecular field model of a ferroelectric crystal has a soft zone-center mode of vibration. The frequency of the mode goes towards zero at the transition point but the mode becomes overdamped very close to the transition. Within the limitations of the moment-expansion method, we see no central peak behavior.

We have applied the effective potential formalism to a simple one-dimensional model of a ferroelectric crystal. The method incorporates quantum effects into a partition function of classical form, which greatly simplifies the calculation. Our results for the nature of the phase transitions, the transition temperatures, and the temperature dependence of the ordering parameter, are all in very good agreement with a full quantum mechanical calculation. Pacs 63.70, 77.80, 64.60.C

We are currently performing Monte Carlo calculations to determine the equation of state of magnesium oxide and related materials. Initially a rigid-ion model was used, but we are presently applying the potential induced breathing model. This has the important advantages of being a first-principles based model which predicts a many-body deviation from the Cauchy relation.