Spherical Lattice Gas

Abstract

The spherical model of a lattice gas has recently been treated by W. Pressman and J. B. Keller, utilizing the relationship between the grand partition function of the spherical lattice gas and the partition function of the spherical model of a ferromagnet. A phase transition in three dimensions was found for the lattice gas, but no description of the transition region was possible. Here we give some features of the canonical partition function for the same model. The equation of state is obtained for all densities and temperatures, and predicts that the pressure remains constant in the transition region. The particle correlations and fluctuations are calculated, and their behavior in this region is shown to be consistent with a phase transition. A physical interpretation of the normal modes of the spherical model indicates that the model contains the general aspects of clustering of particles. The origin of an anomalous behavior of the model, mentioned by Pressman and Keller, consisting of the pressure becoming negative for all temperatures at sufficiently large specific volumes, is described and a method for eliminating it is introduced.