On the method of Yvon in crystal statistics

Abstract Closed-form approximations in crystal statistics have suffered from the defect that no steady series of approximations was available from which the rate of convergence could be assessed. The method of Yvon, based on a cluster-integral type of development, can furnish such a series of approximations. It is shown how to construct the partition functions for such approximations, the key being the use of the Mayer theory for multi-component assemblies. The method is applied to various properties of the Ising model of a ferromagnet and antiferromagnet, and results are obtained which are consistent with those based on series expansions. Previous investigations of Fournet which gave different results are shown to have made use of an insufficient number of terms in the approximation.