Simplicity of condensed matter at its core: Generic definition of a Roskilde-simple system

TL;DR

This paper redefines Roskilde-simple systems using a property of potential energy ordering under uniform scaling, leading to a simplified, nearly one-dimensional phase diagram with invariant properties along isomorphs, validated by simulations.

Contribution

It introduces a new formulation of isomorph theory based on potential energy order preservation, relaxing previous assumptions and providing testable predictions.

Findings

Isomorphs are curves with invariant structure and dynamics.

The density-scaling exponent varies with density.

Simulations confirm the validity of the new formulation.

Abstract

The theory of isomorphs is reformulated by defining Roskilde-simple systems (those with isomorphs) by the property that the order of the potential energies of configurations at one density is maintained when these are scaled uniformly to a different density. Isomorphs remain curves in the thermodynamic phase diagram along which structure, dynamics, and excess entropy are invariant, implying that the phase diagram is effectively one-dimensional with respect to many reduced-unit properties. In contrast to the original formulation of the isomorph theory, however, the density-scaling exponent is not exclusively a function of density and the isochoric heat capacity is not an exact isomorph invariant. A prediction is given for the latter quantity's variation along the isomorphs. Molecular dynamics simulations of the Lennard-Jones and Lennard-Jones Gaussian systems validate the new approach.