High-Activity Perturbation Expansion for the Hard Square Lattice Gas

Details High-Activity Perturbation Expansion for the Hard Square Lattice Gas High-Activity Perturbation Expansion for the Hard Square Lattice Gas

2012-04-19

arxiv.org/abs/1204.4484v1

Physics

Condensed Matter

Statistical Mechanics

9 pages, 5 figures

Scientific paper

We study a system of particles with nearest and next-nearest-neighbour exclusion on the square lattice (hard squares). This model undergoes a transition from a fluid phase at low density to a columnar ordered phase at high density. In this paper we develop a high activity perturbation expansion about the perfectly ordered state and show that the series contains half-integer powers of z, where z is the fugacity associated with each particle. We show that the different terms of the series can be regrouped to get a Mayer-like series of extended objects of arbitrary size. We sum this series to get the exact expansion to order 1/z^{3/2}.

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