The Cluster Variation Method and Some Applications

Abstract

The Cluster Variation Method (CVM) is now recognized as one of the most precise techniques for solving the Ising model when no exact solution is available. Basically, the CVM is a variational technique that consits in minimizing a free energy functional where the exact entropy has been replaced by a linear combination of entropies of finite clusters included in a given maximum cluster. Consequently, its main point is to provide directly an approximation for the free energy, in contrast to other approximate theories. This makes the CVM most useful for the purpose of computing phase diagrams. Besides, its analytical character gives to the CVM, as opposed to numerical simulations, a major advantage when dealing with thermodynamic properties of localized defects.