Crossover between a displacive and an order-disorder phase transition

The phase transition in a three-dimensional array of classical anharmonic o scillators with harmonic nearest-neighbor coupling (discrete o(4) model) is studied by Monte Carlo (MC) simulations and by analytical methods. The mod el allows us to choose a single dimensionless parameter a determining compl etely the behavior of the system. Changing a from 0 to + infinity allows to go continuously from the displacive to the order-disorder limit. We calcul ate the transition temperature T-c and the temperature dependence of the or der parameter down to T = 0 for a wide range of the parameter a. The T-c fr om MC calculations shows an excellent agreement with the known asymptotic v alues for small and large a. The obtained MC results are further compared w ith predictions of the mean-field and independent-mode approximations as we ll as with predictions of our own approximation scheme. In this approximati on, we introduce an auxiliary system, which yields approximately the same t emperature behavior of the order parameter, but allows the decoupling of th e phonon modes. Our approximation gives the value of T-c within an error of 5% and satisfactorily describes the temperature dependence of the order pa rameter for all values of a.