Direct determination of liquid phase coexistence by Monte Carlo simulations

A formalism to determine coexistence points by means of Monte Carlo simulations is presented. The general idea of the method is to perform a simulation simultaneously in several unconnected boxes which can exchange particles. At equilibrium, most of the boxes will be occupied by a homogeneous phase. The compositions of these boxes yield coexisting points on the binodal. However, since the overall composition is fixed, at least one of the boxes will contain an interface. We show that this does not affect the results, provided that the interface has no net curvature. We coin the name "Helmholtz-ensemble method," because the method is related to the well-known Gibbs-ensemble method, but the volume of the boxes is constant. Since the box volumes are constant, we expect that this method will be particularly useful for lattice models. The accuracy of the Helmholtz-ensemble method is benchmarked against known coexistence curves of the three-dimensional Ising model with excellent results.