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

TL;DR

This study uses Monte Carlo simulations to explore the phase diagram of hard rectangles with non-integer aspect ratios on a square lattice, revealing multiple phases and transition behaviors.

Contribution

It provides new insights into phase transitions of non-integer aspect ratio rectangles, including the existence of various ordered phases and their critical properties.

Findings

Identified isotropic, nematic, columnar, and high-density phases.

Determined the minimum aspect ratio for phase existence.

Numerically obtained critical exponents for phase transitions.

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.