Phase Boundaries of Bulk 2D Rhombi

TL;DR

This study uses replica exchange Monte Carlo simulations to map the phase diagram of 2D hard rhombi, revealing various fluid and solid phases depending on shape and density, including novel aperiodic structures.

Contribution

First comprehensive simulation-based phase diagram of 2D hard rhombi across shape variations, identifying new aperiodic and long-range ordered phases.

Findings

Identified multiple fluid and solid phases, including isotropic, nematic, rhombatic, and aperiodic structures.

Discovered a transition to long-range six-fold symmetry structures near 60° shape.

Observed melting into hexatic and isotropic phases from complex solid structures.

Abstract

We conducted replica exchange Monte Carlo simulations to investigate the phase diagram of identical hard rhombi systems in two dimensions. The rhombi shape varies from nearly square-like, as their minor angle a approaches 90 degrees, to needle-like, as it approaches 0 degrees. For angles near 90 degrees, we observe an isotropic fluid, a rhombatic fluid, a rotator phase, and a columnar space-filling structure with increasing density. Conversely, as a approaches 0 degrees, the results resemble the needle limit. Even for angles as small as a = 20 degrees, we still obtain isotropic, nematic, and rhombatic fluids before reaching a rhombic solid, but the nematic phase gains importance with decreasing a. At a approximately 60 degrees, aperiodic space-filling structures with long-range six-fold orientational symmetry dominate over periodic candidates such as the rhombic and rhombille. This aperiodic solid undergoes a melting process leading to a phase with quasi-long-range six-fold orientational symmetry, a hexatic fluid, before reaching the isotropic phase.