Van der Waals loops and the melting transition in two dimensions

TL;DR

This paper investigates the presence of van der Waals loops in two-dimensional systems and questions their implication for the nature of melting, providing new simulation data and comparisons with the 2D Ising model.

Contribution

It provides accurate equilibrium pressure-volume curves for 2D hard disks and critically examines the link between van der Waals loops and first-order melting transitions.

Findings

Van der Waals loops are observed in finite 2D hard disk systems.

Existence of van der Waals loops does not necessarily imply a first-order transition.

Comparison with 2D Ising model suggests loops may persist at criticality without indicating a first-order transition.

Abstract

Evidence for the existence of van der Waals loops in pressure p versus volume v plots has for some time supported the belief that melting in two dimensions is a first order phase transition. We report rather accurate equilibrium p(v) curves for systems of hard disks obtained from long Monte Carlo simulations. These curves, obtained in the constant volume ensemble, using periodic boundary conditions, exhibit well defined van der Waals loops. We illustrate their existence for finite systems that are known to undergo a continuous transition in the thermodynamic limit. To this end, we obtain magnetization m versus applied field curves from Monte Carlo simulations of the 2D Ising model, in the constant m ensemble, at the critical point. Whether van der Waals loops for disk systems behave in the thermodynamic limit as they do for the 2D Ising model at the critical point cannot be ruled out. Thus, the often made claim that melting in 2D is a first order phase transition, based on the evidence that van der Waals loops exist, is not sound.