Mean Field Theory and Infinite Dimensionality in Widom—Rowlinson Model

Abstract

It is known for the Ising model that the mean field theory describes exactly the limit of infinite dimensionality in the one‐phase region. It is shown in this article that the same statement applies also to the Widom—Rowlinson model of penetrable cubes. This model has nonpairwise‐additive, many‐body interactions such as one finds in the ionic solution theory. Mayer's cluster expansion scheme is used to show that the equation of state in the limit of infinite dimensionality is identical to the mean field result.