Phase transitions in a system of hard rectangles on the square lattice

Abstract

The phase diagram of a system of monodispersed hard rectangles of size $m\times mk$ on a square lattice is numerically determined for $m=2,3$ and aspect ratio $k=1,2,\dots ,7$. We show the existence of a disordered phase, a nematic phase with orientational order, a columnar phase with orientational and partial translational order, and a solid-like phase with sublattice order, but no orientational order. The asymptotic behavior of the phase boundaries for large $k$ are determined using a combination of entropic arguments and a Bethe approximation. This allows us to generalize the phase diagram to larger $m$ and $k$, showing that for $k\ge 7$, the system undergoes three entropy driven phase transitions with increasing density. The nature of the different phase transitions are established and the critical exponents for the continuous transitions are determined using finite size scaling.

16 pages, 20 figures

References in corpus (5)

• Monte Carlo simulations of 2d hard core lattice gases
• Determination of the Critical Exponents for the Isotropic-Nematic Phase Transition in a System of Long Rods on Two-dimensional Lattices: Universality of the Transition
• Critical behavior of long straight rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations
• Orientational correlations and the effect of spatial gradients in the equilibrium steady state of hard rods in 2D : A study using deposition-evaporation kinetics
• Restricted orientation "liquid crystal" in two dimensions: Isotropic-nematic transition or liquid-gas (?)

Cited by in corpus (35)

• 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
• Monolayers of hard rods on planar substrates: I. Equilibrium
• The isotropic-nematic transition for hard rods on a three--dimensional (3D) cubic lattice
• Stability of columnar order in assemblies of hard rectangles or squares
• Different phases of a system of hard rods on three dimensional cubic lattice
• 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
• High-Activity Expansion for the Columnar Phase of the Hard Rectangle Gas
• Phase Transitions in Hardcore Lattice Gases on the Honeycomb Lattice
• Ordering of hard rectangles in strong confinement
• 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
• Phase transitions in systems of hard rectangles with non-integer aspect ratio
• Multiple Exclusion Statistics
• A scale-bridging modeling approach for anisotropic organic molecules at patterned semiconductor surfaces
• The phase transition from nematic to high-density disordered phase in a system of hard rods on a lattice
• Ordering transitions of weakly anisotropic hard rods in narrow slit-like pores
• Phase diagram of a bidispersed hard rod lattice gas in two dimensions
• Polydispersed rods on the square lattice
• 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
• Three stable phases and thermodynamic anomaly in a binary mixture of hard particles
• Entropy of different phases formed by soft rods
• Hard core lattice gas with third next-nearest neighbor exclusion on triangular lattice: one or two phase transitions?
• Diffusion dynamics and steady states of systems of hard rods on the square lattice
• Thermodynamic behavior of binary mixtures of hard spheres: Semianalytical solutions on a Husimi lattice built with cubes
• Nematic and gas-liquid transitions for sticky rods on square and cubic lattices
• Polyomino Models of Surface Supramolecular Assembly: Design Constraints and Structural Selectivity
• Phases of the hard-plate lattice gas on a three-dimensional cubic lattice
• Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases
• Percolation in semicontinuum geometries