What do Landau free energies really look like for structural phase transitions?

Abstract

Landau free-energy expansions are commonly used to describe systems undergoing structural phase transitions. The Landau free energy of a model solid with an anharmonic potential (often a double well) at each site and mean-field-like inter-site coupling has been calculated both analytically and from molecular dynamics simulation. The calculated free-energy function is not well described by a simple polynomial in the order parameter. This result is not due to critical fluctuations in the Ginzburg interval. If, however, such a polynomial is used the coefficient of the fourth-order term is found to be highly temperature dependent. For a certain range of model parameters this coefficient is small relative to that of the second-order term. These observations help to explain the occurrence of 'non-critical, non-standard' values of the exponent beta in the variation of the order parameter, x, with temperature: x varies as (T_c-T)^beta . More importantly they also help to explain why so many natural systems behave in a tricritical-type manner with beta approximately=¹/₄.