Phase transitions in systems of hard rectangles with non-integer aspect ratio

Abstract

We investigate, using Monte Carlo simulations, the phase diagram of a system of hard rectangles of size $m\times mk$ on a square lattice when the aspect ratio $k$ is a non-integer. The existence of a disordered isotropic phase, a nematic with only orientational order, a columnar phase with orientational and partial translational order, and a high density phase with no orientational order is shown. The high density phase is a solid-like sublattice phase only if the length and width of the rectangles are not mutually prime, else, it is an isotropic phase. The minimum value of $k$ beyond which the nematic and columnar phases exist are determined for $m=2$ and $3$. The nature of the transitions between different phases is determined, and the critical exponents are numerically obtained for the continuous transitions.

arXiv comment6 pages, 6 figures

References in corpus (12)

• Classical dimers on the triangular lattice
• On the orientational ordering of long rods on a lattice
• The nematic-disordered phase transition in systems of long rigid rods on two dimensional lattices
• 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
• 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
• Restricted orientation "liquid crystal" in two dimensions: Isotropic-nematic transition or liquid-gas (?)
• Asymptotic Behavior of the Isotropic-Nematic and Nematic-Columnar Phase Boundaries for the System of Hard Rectangles on a Square lattice
• Entropy-driven phase transition in a polydisperse hard-rods lattice system
• Re-entrant Disordered Phase in a System of Repulsive Rods on a Bethe-like Lattice
• Polydispersed rods on the square lattice

Cited by in corpus (13)

• 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
• 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 diagram of a system of hard cubes on the cubic lattice
• Estimating the Critical Parameters of the Hard Square Lattice Gas Model
• The phase transition from nematic to high-density disordered phase in a system of hard rods on a lattice
• Phase diagram of a bidispersed hard rod lattice gas in two dimensions
• The freezing phase transition in hard core lattice gases on triangular lattice with exclusion up to seventh next-nearest neighbor
• Entropy of different phases formed by soft rods
• Diffusion dynamics and steady states of systems of hard rods on the square lattice
• Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases