Note: Melting criterion for soft particle systems in two dimensions

TL;DR

This paper proposes a simple, near-universal melting criterion for two-dimensional soft particle systems based on the ratio of transverse sound velocity to thermal velocity, enabling straightforward melting line estimation.

Contribution

It introduces a new melting criterion for 2D soft particle systems, combining BKT theory with sound velocity ratios, and demonstrates its application to Yukawa systems.

Findings

The ratio of transverse to thermal velocity is approximately 4.3 at melting.

The criterion provides accurate estimates of melting lines in 2D soft systems.

Application to Yukawa systems validates the criterion's effectiveness.

Abstract

A simple criterion for melting of two-dimensional crystals with soft long-ranged interactions is proposed. It states that the ratio of the transverse sound velocity of an ideal crystalline lattice to the thermal velocity is a quasi-universal number close to $4.3$ at melting. This criterion is arrived by reference to the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young theory of two-dimensional melting, combined with the observation that the ratio of transverse-to-longitudinal sound velocities is small in the soft interaction limit. Application of this criteria allows estimating melting lines in a simple yet relatively accurate manner. Two-dimensional weakly screened Yukawa systems represent one relevant example considered.