van der Waals loops and the melting transition in two dimensions

Evidence for the existence of van der Waals loops in pressure p versus volu me v plots has for some time supported the belief that melting in two dimen sions (2D) is a first-order phase transition. We report rather accurate equ ilibrium p(v) curves for systems of hard disks obtained from long Monte Car lo simulations. These curves, obtained in the constant volume ensemble, usi ng 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 two-dimensional Ising model, in the constant m ensemble, at the critic al point. Whether van der Waals loops for disk systems behave in the L-->in finity limit as they do for the two-dimensional Ising model at the critical point cannot be ruled out. Thus, the often made claim that melting in 2D i s a first-order phase transition, based on the evidence that van der Waals loops exist, is not sound. [S1063-651X(99)01603-7].