Crossover between a displacive and an order-disorder phase transition

The phase transition in a three-dimensional array of classical anharmonic oscillators with harmonic nearest-neighbor coupling (discrete φ 4 model) is studied by Monte Carlo (MC) simulations and by analytical methods. The model allows us to choose a single dimensionless parameter a determining completely the behavior of the system. Changing a from 0 to + ∞ allows to go continuously from the displacive to the order-disorder limit. We calculate the transition temperature T c and the temperature dependence of the order parameter down to T = 0 for a wide range of the parameter a. The T c from MC calculations shows an excellent agreement with the known asymptotic values for small and large a. The obtained MC results are further compared with predictions of the mean-field and independent-mode approximations as well as with predictions of our own approximation scheme. In this approximation, we introduce an auxiliary system, which yields approximately the same temperature behavior of the order parameter, but allows the decoupling of the phonon modes. Our approximation gives the value of T c within an error of 5% and satisfactorily describes the temperature dependence of the order parameter for all values of a.