Exactly soluble models for distortive structural phase transitions

We examine three exactly soluble models for systems undergoing a structural phase transition. Two models are described by a lattice-dynamic hamiltonian, the phase transition being driven by a spherical constraint in one case and by a long-range anharmonic interaction in the other. Finally, we treat a continuous model based on an effective free energy for the long-wavelength fluctuations of the order-parameter field, which may be obtained by eliminating the other non-critical degrees of freedom. The static critical exponents are those of the spherical Kac model in all three cases, whereas the dynamic critical behaviour strongly depends on the time reversal properties of the underlying equation of motion.