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.

6 pages, 6 figures

References in corpus (4)

• 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
• 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
• Polydispersed rods on the square lattice

Cited by in corpus (3)

• The isotropic-nematic transition for hard rods on a three--dimensional (3D) cubic lattice
• Phase diagram of a system of hard cubes on the cubic lattice
• Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases