Lattice-switch Monte Carlo method

We present a Monte Carlo method for the direct evaluation of the difference between the free energies of two crystal structures. The method is built o n a lattice-switch transformation that maps a configuration of one structur e onto a candidate configuration of the other by "switching'' one set of la ttice vectors for the other, while keeping the displacements with respect t o the lattice sites constant. The sampling of the displacement configuratio ns is biased, multicanonically, to favor paths leading to gateway arragemen ts fbr which the Monte Carte switch to the candidate configuration will be accepted. The configurations of both structures can then be efficiently sam pled in a single process, and the difference between their free energies ev aluated from their measured probabilities. We explore and exploit the metho d in the context of extensive studies of systems of hard spheres. We show t hat the efficiency of the method is controlled by the extent to which the s witch conserves correlated microstructure. We also show how, microscopicall y, the procedure works: the system finds gateway arrangements which fulfill the sampling bias intelligently. We establish, with high precision, the di fferences between the free energies of the two close packed structures (fce and hcp) in both the constant density and the constant pressure ensembles. PACS number(s): 05.10.Ln, 65.50.+m, 64.30.Kb.