A classical theory of hard squares

Abstract

A simple phenomenological theory of the hard-square lattice gas is obtained by analyzing a low-order corner transfer matrix variational approximation. The free energy is of Landau type and expressions are obtained for the order parameter and densities. In this approximation, the model exhibits a critical point atz c =4(3 + 2√3)/9 with critical exponents given by the classical values: α=0disc,β=1/2, γ=1, δ=3.