2D Melting: From Liquid-Hexatic Coexistence to Continuous Transitions

TL;DR

This study explores the phase transitions in two-dimensional particle systems, revealing a transition from liquid-hexatic coexistence to continuous melting behavior depending on interaction parameters, with implications for understanding 2D melting scenarios.

Contribution

It demonstrates how the melting scenario in 2D systems varies with interaction range, unifying the hard-disk and KTHNY melting behaviors through systematic simulations.

Findings

Hard-disk melting scenario applies for large n (n ≥ 6).

For n < 6, the liquid-hexatic transition is continuous, aligning with KTHNY theory.

Yukawa particles can exhibit either melting scenario depending on parameters.

Abstract

The phase diagram of two-dimensional continuous particle systems is studied using Event-Chain Monte Carlo. For soft disks with repulsive power-law interactions $\propto r^{-n}$ with $n \gtrsim 6$, the recently established hard-disk melting scenario ($n \to \infty$) holds: a first-order liquid-hexatic and a continuous hexatic-solid transition are identified. Close to $n = 6$, the coexisting liquid exhibits very long orientational correlations, and positional correlations in the hexatic are extremely short. For $n\lesssim 6$, the liquid-hexatic transition is continuous, with correlations consistent with the Kosterlitz-Thouless-Halperin-Nelson-Yong (KTHNY) scenario. To illustrate the generality of these results, we demonstrate that Yukawa particles likewise may follow either the KTHNY or the hard-disk melting scenario, depending on the Debye-H\"uckel screening length as well as on the temperature.