Direct evaluation of multicomponent phase equilibria using flat-histogram methods

We present a method for directly locating density-driven phase transitions in multicomponent systems. Phase coexistence conditions are determined through manipulation of a total density probability distribution evaluated over a density range that includes both coexisting phases. Saturation quantities are determined through appropriate averaging of density-dependent mean values of a given property of interest. We discuss how to implement the method in both the grand-canonical and isothermal-isobaric semigrand ensembles. Calculations can be conducted using any of the recently introduced flat-histogram techniques. Here, we combine the general algorithm with a transition-matrix approach to produce an efficient self-adaptive technique for determining multicomponent phase equilibrium properties. To assess the performance of the new method, we generate phase diagrams for a number of binary and ternary Lennard-Jones mixtures.