Cluster Approximations for Order-Disorder-Type Hydrogen-Bonded Ferroelectrics. I. Small Clusters

Abstract

A high-temperature cluster series is derived for the partition function of an order-disorder-type hydrogen-bonded ferroelectric crystal, taking into account a simplified interaction between protons as well as the overlap of the protonic wave functions between the two sites in a hydrogen bond. The zero-order result is the Weiss molecular-field approximation, and the two-particle-cluster result reduces in the classical limit to the Bethe treatment of the Ising model. The specific properties of crystal lattices can be taken into account in higher order terms. The results of the above approximations as well as the results of an "Oguchi"-type treatment, valid at all temperatures, are compared with exact solutions in the case of a simple soluble model.