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arXiv · 1204.4484

High-Activity Perturbation Expansion for the Hard Square Lattice Gas

Kabir Ramola·Deepak Dhar
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Abstract

We study a system of particles with nearest and next-nearest-neighbour 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 $n$-th 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 $1/z^{3/2}$.

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BibTeXRIS

Kabir Ramola, Deepak Dhar. 2012-08-04. High-Activity Perturbation Expansion for the Hard Square Lattice Gas. https://doi.org/10.1103/physreve.86.031135

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