Comparison of mean-field theories for a model ferroelectric

The equilibrium properties of a model ferroelectric have been investigated in classical approximation. For the displacive limit and $T<\mathrm{}{T}_c$ strong indications are given that even for short-range interaction the self-consistent-phonon mean-field approximation describes the exact temperature behavior outside a region $\frac{|T-T_c|}{T_c}$ which tends to zero in the very displacive limit. In the order-disorder limit, high-and low-temperature expansions as well as a comparison of free energies show that a Curie-Weiss (independent-site) mean-field approximation, though not being exact, is to be preferred over a self-consistent-phonon approach.