Freezing and re-entrant melting of hard discs in a one-dimensional potential:\\ Predictions based on a pressure-balance equation

TL;DR

This paper theoretically predicts the phase diagram of a 2D hard disc system under a 1D external potential, capturing freezing and re-entrant melting phenomena using a pressure-balance approach aligned with simulation results.

Contribution

It introduces a pressure-balance equation based on density functional theory to predict phase behavior of hard discs in a 1D potential, including re-entrant melting.

Findings

Phase diagram agrees with Monte Carlo simulations.

Re-entrant melting explained by registration effects.

Pressure-balance approach effectively predicts phase transitions.

Abstract

We investigate theoretically the freezing behaviour of a two-dimensional (2D) system of hard discs on a one-dimensional (1D) external potential (typically called laser-induced freezing). As shown by earlier theoretical and numerical studies, one observes freezing of the modulated liquid upon increase of the substrate potential amplitude, and re-entrant melting back into the modulated liquid when the substrate potential amplitude is increased even further. The purpose of our present work is to calculate the freezing and re-entrant melting phase diagram based on information from the bulk system. To this end, we employ an integrated pressure-balance equation derived from density functional theory [Phys. Rev. E \textbf{101}, 012609 (2020)]. Furthermore, we define a measure to quantify the influence of registration effects that qualitatively explain re-entrant melting. Despite severe approximations, the calculated phase diagram shows good agreement with the known phase diagram obtained by Monte Carlo simulations.