Columnar Order and Ashkin-Teller Criticality in the Hard Square Lattice Gas
Kabir Ramola, LPTMS Orsay
The lattice gas model of particles with nearest and next-nearest-neighbour exclusion on a square lattice (hard squares) undergoes a transition from a fluid phase at low density to a columnar ordered phase at high density. The high-activity series for this model is a singular perturbation series in powers of 1/z, where z is the fugacity associated with each particle. We show that the different terms of the series need to be regrouped to get a Mayer-like series for a polydisperse system of interacting vertical rods. We also analyse the nature of the phase transition as a function of density in this system. We argue that the critical properties of the model are that of a more general Ashkin-Teller model. We employ Monte Carlo simulations to study the correlations between various quantities in the system to get a fairly precise estimate of the position of the transition on the Ashkin-Teller critical line.