THE LANDAU FREE-ENERGY OF THE 3-DIMENSIONAL PHI(4) MODEL IN WIDE TEMPERATURE INTERVALS

The range of validity of Landau free-energy potentials with the usual approximation of constant coefficients for terms higher than quadratic has recently been questioned (J. Phys.: Condens. Matter 1 (1989) 8327). The frequent observation in real systems, within large temperature intervals, clearly outside any possible critical region, of power laws of the type \T(c) - T\b for the order parameter has also been pointed out as an indication that certain simple general features in phase transitions, not related at all to critical phenomena, are beyond the usual approximations included in a Landau free-energy expansion. In particular, the value of the exponent b has been proposed to be related to the displacive and order-disorder degree of the system. In order to elucidate these questions, the temperature dependence of the Landau free energy corresponding to the three-dimensional THETA4 model has been investigated using a straightforward Monte Carlo method. Different model parameters have been considered, ranging from typical displacive parameters to those approaching a pure order-disorder system. Following its formal definition, the Landau free energy at each temperature has been directly derived from the order parameter distribution in a Metropolis statistical sample. In contrast with other numerical methods used in previous literature, no approximation is introduced in the calculation, except inherent to the numerical method employed. It is shown that the temperature dependence of the Landau potential coefficients follows smooth simple laws that are outside the usual assumptions in Landau theory and can be related to the order-disorder degree of the system. The quadratic coefficient in the Landau potential exhibits a linear temperature dependence in large temperature intervals but shows a marked change in slope about the transition temperature. The quartic coefficient is shown to depend on temperature as strongly as the quadratic coefficient having a minimum around the transition point. The strong temperature dependence of this quartic coefficient is responsible for the 'non-classical' behaviour of the order parameter, which can be described by a power law.