Estimating the Critical Parameters of the Hard Square Lattice Gas Model

Abstract

The hard square lattice gas model on a square lattice is known to undergo a continuous phase transition from a low density fluid-like phase to high density phase with columnar or smectic order. We estimate the critical activity $z_c$ by calculating, within an approximation scheme, the interfacial tension between two differently ordered columnar phases, and then setting it to zero. The approximation scheme allows for the ordered phases to have multiple defects and the interface between the ordered phases to have overhangs. We estimate $z_c=105.35$, which is in good agreement with existing Monte Carlo simulation results of $z_c\approx 97.5$, and is an improvement over earlier best estimates of $z_c=54.87$ and $z_c=135.63$.

19 pages, 10 figures

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• On the accuracy of first-principles lateral interactions: Oxygen at Pd(100)
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Cited by in corpus (10)

• Entropy of fully packed hard rigid rods on $d$-dimensional hyper-cubic lattices
• Different phases of a system of hard rods on three dimensional cubic lattice
• Phase transitions in a system of hard $Y$-shaped particles on the triangular lattice
• Liquid-Hextic-Solid Phase Transition of a Hard-Core Lattice Gas with Third Neighbor Exclusion
• Phase diagram of a system of hard cubes on the cubic lattice
• Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases
• The columnar-disorder phase boundary in a mixture of hard squares and dimers
• Hard core lattice gas with third next-nearest neighbor exclusion on triangular lattice: one or two phase transitions?
• Phases of the hard-plate lattice gas on a three-dimensional cubic lattice
• Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases