Multiple Phase Transitions in Extended Hard Core Lattice Gas Models in Two Dimensions

Abstract

We study the $k$-NN hard core lattice gas model in which the first $k$ next nearest neighbor sites of a particle are excluded from occupation by other particles on a two dimensional square lattice. This model is the lattice version of the hard disc system with increasing $k$ corresponding to decreasing lattice spacing. While the hard disc system is known to undergo a two step freezing process with increasing density, the lattice model has been known to show only one transition. Here, based on Monte Carlo simulations and high density expansions of the free energy and density, we argue that for $k=4,10,11,\mathrm{14...}$, the lattice model undergoes multiple transitions with increasing density. Using Monte Carlo simulations, we confirm the same for $k=4,\dots ,11$. This, in turn, resolves an existing puzzle as to why the 4-NN model has a continuous transition against the expectation of a first order transition.

19 pages, 23 figures

References in corpus (3)

• Monte Carlo simulations of 2d hard core lattice gases
• On the accuracy of first-principles lateral interactions: Oxygen at Pd(100)
• Equation of state for hard square lattice gases

Cited by in corpus (29)

• 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
• Arrested States in Persistent Active Matter: Gelation without Attraction
• Stability of columnar order in assemblies of hard rectangles or squares
• Different phases of a system of hard rods on three dimensional cubic lattice
• Entropy of fully packed hard rigid rods on $d$-dimensional hyper-cubic lattices
• The High Density Phase of the $k$-NN Hard Core Lattice Gas Model
• 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
• 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
• Estimating the Critical Parameters of the Hard Square Lattice Gas Model
• Phase transitions in systems of hard rectangles with non-integer aspect ratio
• Motion of active tracer in a lattice gas with cross-shaped particles
• Transfer-matrix study of a hard-square lattice gas with two kinds of particles and density anomaly
• Phase diagram of a bidispersed hard rod lattice gas in two dimensions
• Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases
• Polydispersed rods on the square lattice
• 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
• Three stable phases and thermodynamic anomaly in a binary mixture of hard particles
• Hard core lattice gas with third next-nearest neighbor exclusion on triangular lattice: one or two phase transitions?
• Polymers with nearest- and next nearest-neighbor interactions on the Husimi lattice
• Thermodynamic behavior of binary mixtures of hard spheres: Semianalytical solutions on a Husimi lattice built with cubes
• Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases
• Condensation and crystal nucleation in a lattice gas with a realistic phase diagram
• Phases of the hard-plate lattice gas on a three-dimensional cubic lattice
• Crystalline ordering and large fugacity expansion for hard core lattice particles