On the accuracy of the melting curves drawn from modelling a solid as an elastic medium

TL;DR

This paper introduces a computationally efficient method combining the Lindemann criterion with elastic continuum modeling to reliably predict melting curves in systems with complex interparticle potentials.

Contribution

It presents a novel approach to determine melting lines in classical many-body systems with softened or adjustable potentials, reducing computational effort.

Findings

Method compares favorably with the self-consistent harmonic approximation.

Reliable melting-curve topologies obtained with negligible computational effort.

Applicable to systems with Gaussian-shaped two-body repulsion.

Abstract

An ongoing problem in the study of a classical many-body system is the characterization of its equilibrium behaviour by theory or numerical simulation. For purely repulsive particles, locating the melting line in the pressure-temperature plane can be especially hard if the interparticle potential has a softened core or contains some adjustable parameters. A method is hereby presented that yields reliable melting-curve topologies with negligible computational effort. It is obtained by combining the Lindemann melting criterion with a description of the solid phase as an elastic continuum. A number of examples are given in order to illustrate the scope of the method and possible shortcomings. For a two-body repulsion of Gaussian shape, the outcome of the present approach compares favourably with the more accurate but also more computationally demanding self-consistent harmonic approximation.