Entropy derivation for cluster methods in non-Bravais lattices

TL;DR

This paper reformulates entropy derivation for cluster methods using a self-consistent probability product, extending the approach to non-Bravais lattices like BCC and FCC crystals.

Contribution

It introduces a new self-consistent product formulation of entropy for cluster methods, enabling extension to non-Bravais lattices.

Findings

Provides a graphical representation for the product approach.

Successfully extends the method to interstitial sites in BCC and FCC lattices.

Offers insights into the approximations in cluster-variation methods.

Abstract

The derivation of entropy for cluster methods is reformulated by constructing the probability of a given particle (spin) configuration as a self-consistent product of cluster configuration probabilities. This approach gives an insight into the nature of underlying approximations involved at different levels of the cluster-variation method. The graphical representation of the product allows us to extend this method for non-Bravais lattices as it is demonstrated on interstitial sites of body-centered- and face-centered-cubic crystals.