Melting in Monolayers : Hexatic and Fluid Phases

TL;DR

This study uses Monte Carlo simulations to explore how the melting behavior of a two-dimensional monolayer of particles varies with different inverse power law interactions, revealing diverse melting mechanisms and aligning with KTHNY theory for certain cases.

Contribution

It provides a comprehensive analysis of 2D melting across a range of interaction potentials, connecting empirical transition curves with theoretical predictions.

Findings

Melting mechanisms vary with the interaction exponent n.

Good agreement with KTHNY theory for n ≤ 3.

Empirical transition curves match simulation results.

Abstract

There are strong evidences that the melting in two dimensions depends crucially on the form and range of the interaction potentials between particles. We study with Monte Carlo simulations the phase diagram and the melting of a monolayer of point-particles interacting with repulsive Inverse Power Law Interactions, $V(r)=Q^2(\sigma/r)^n$ where $n$ can take any real positive value ($n$-OCP monolayer). As $n$ is varied from 0 to $\infty$ (Hard Disks), including Coulomb ($n=1$) and Dipolar ($n=3$), melting occurs with different mechanisms and the overall picture permits to understand the diversity of mechanisms found experimentally or in computer simulations for 2D melting. The empirical transition curves for $n\leq 3$ and the excellent qualitative and semi-quantitative agreements with the KTHNY theory found for the melting of $n$-OCP monolayers with $n\leq 3$ are the main results of the present work.