High-Activity Perturbation Expansion for the Hard Square Lattice Gas

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 $1/z^{3/2}$.

8 pages, 6 figures

References in corpus (3)

• On the orientational ordering of long rods on a lattice
• Monte Carlo simulations of 2d hard core lattice gases
• Lattice gas description of pyrochlore and checkerboard antiferromagnets in a strong magnetic field

Cited by in corpus (25)

• Phase transitions in a system of hard rectangles on the square lattice
• Multiple Phase Transitions in Extended Hard Core Lattice Gas Models in Two Dimensions
• Columnar order and Ashkin-Teller criticality in mixtures of hard-squares and dimers
• Asymptotic Behavior of the Isotropic-Nematic and Nematic-Columnar Phase Boundaries for the System of Hard Rectangles on a Square lattice
• Stability of columnar order in assemblies of hard rectangles or squares
• The High Density Phase of the $k$-NN Hard Core Lattice Gas Model
• 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
• High-Activity Expansion for the Columnar Phase of the Hard Rectangle Gas
• Phase Transitions in Hardcore Lattice Gases on the Honeycomb Lattice
• Phase transitions in a system of hard $Y$-shaped particles on the triangular lattice
• Phase diagram of a system of hard cubes on the cubic lattice
• Estimating the Critical Parameters of the Hard Square Lattice Gas Model
• Motion of active tracer in a lattice gas with cross-shaped particles
• Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases
• The freezing phase transition in hard core lattice gases on triangular lattice with exclusion up to seventh next-nearest neighbor
• 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?
• Condensation and crystal nucleation in a lattice gas with a realistic phase diagram
• Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases
• Highly confined mixtures of parallel hard squares: A Density Functional Theory study
• Phases of the hard-plate lattice gas on a three-dimensional cubic lattice
• Lattice and PT symmetries in tensor-network renormalization group: Case study of a hard-square lattice gas model
• Upper bounds for the connective constant of weighted self-avoiding walks
• Crystalline ordering and large fugacity expansion for hard core lattice particles