The Direct Correlation Function of an Inhomogeneous Lattice Gas

Two terms beyond mean field approximation are obtained for the direct correlation function of a general lattice gas. Use is made of Mayer's cluster expansion extended to inhomogeneous systems. The resulting expression is as simple and as readily applicable as the mean field approximation. It can deal with ferromagnetic or antiferromagnetic interaction, below or above transition temperature, with or without far neighbor interactions. Specializing to an Ising model its accuracy is better than that obtained by the Bethe method. A new high temperature expansion for lattice gases is discovered. In the new expansion scheme only doubly-connected graphs need to be considered. As far as the counting of graphs is concerned the present method is the simplest among all the existing series expan· sions for lattice gas.