Statistical thermodynamics of uniaxial ferroelectric: exactly solved model

Abstract

A detailed analysis of the thermodynamic properties of uniaxial ferroelectrics is carried out within the framework of an exactly soluble model with an infinite radius of interactions. The free energy of a ferroelectric in a power series in the order parameter is expanded and it is shown that all the coefficients of even degree depend strongly on temperature, including the change of their signs at temperatures below the Curie point. The equation of state of a ferroelectric in an external field is derived. A relationship between the width of the zone of metastable states of the ferroelectric and the temperature interval is established. An expression is derived for the height of the energy barrier separating the metastable and stable states of a ferroelectric. The results obtained within the framework of the exact solution of the model are compared with the results within the framework of the Landau-Devonshire phenomenological theory. It is shown that for dimensionless temperatures any Landau-like polynomial approximations for free energy lead to significant errors both in calculating the free energy and in calculating the equilibrium values of the order parameter.