High-activity perturbation expansion for the hard square lattice gas.

We study a system of particles with nearest- and next-nearest-neighbor exclusion on the square lattice (hard squares). This system undergoes a transition from a fluid phase at low density to a columnar-ordered phase at high density. We develop a systematic high-activity perturbation expansion for the free energy per site about a state with perfect columnar order. We show that the different terms of the series can be regrouped to get a Mayer-like series for a polydisperse system of interacting vertical rods in which the nth term is of order z(-(n+1)/2), where z is the fugacity associated with each particle. We sum this series to get the exact expansion to order 1/z(3/2).