Three-step melting of hard superdisks in two dimensions

TL;DR

This study investigates the melting behavior of two-dimensional hard superdisks, revealing a unique three-step melting process involving two mesophases, expanding understanding of phase transitions in anisotropic particle systems.

Contribution

It introduces a three-step melting scenario for 2D hard superdisks, including the discovery of a rhombatic mesophase with $D_2$ symmetry, which was not previously documented.

Findings

Melting of superdisks involves two mesophases: hexatic and rhombatic.

A three-step melting process was observed for dual-shape superdisks.

The study links shape anisotropy to complex melting behaviors.

Abstract

We explore the link between the melting scenarios of two-dimensional systems of hard disks and squares through replica-exchange Monte Carlo simulations of hard superdisks. The well-known melting scenarios are observed in the disk and square limits, while we observe an unusual three-step scenario for dual-shapes. We find that two mesophases mediate the melting: a hexatic phase and another fluid phase with a $D_2$ local symmetry, we call it rhombatic, where both bond and particle orientational orders are quasi-long-range. Our results show that not only can the melting process of liquid-crystal forming molecules be complicated, where elongated shapes stabilize several mesophases, but also that of anisotropic quasispherical molecules.