The High Density Phase of the $k$-NN Hard Core Lattice Gas Model

Abstract

The $k$-NN hard core lattice gas model on a square lattice, in which the first $k$ next nearest neighbor sites of a particle are excluded from being occupied by another particle, is the lattice version of the hard disc model in two dimensional continuum. It has been conjectured that the lattice model, like its continuum counterpart, will show multiple entropy-driven transitions with increasing density if the high density phase has columnar or striped order. Here, we determine the nature of the phase at full packing for $k$ up to $820302$. We show that there are only eighteen values of $k$, all less than $k=4134$, that show columnar order, while the others show solid-like sublattice order.

References in corpus (2)

• Monte Carlo simulations of 2d hard core lattice gases
• Stability of columnar order in assemblies of hard rectangles or squares

Cited by in corpus (10)

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• Liquid-Hextic-Solid Phase Transition of a Hard-Core Lattice Gas with Third Neighbor Exclusion
• Phase Transitions in Hardcore Lattice Gases on the Honeycomb Lattice
• Phase diagram of a system of hard cubes on the cubic lattice
• Estimating the Critical Parameters of the Hard Square Lattice Gas Model
• 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
• 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