Parallel Replica Exchange Monte Carlo Applied to Hard Systems

In this chapter we show how the replica exchange Monte Carlo algorithm can be used to study hard systems, i.e. systems composed by hard particles such as spheres, ellipsoids, disks, and ellipses, among others. The method is based on the definition of an extended ensemble which usually uses temperature as the expansion variable. This way, the low temperature replicas perform local sampling on the configuration space while high temperature replicas produce large jumps. The replica swap moves allow for a low temperature replica to heat, reach another region of configuration space, and cool back, enhancing the sampling of low-temperature, uneven free energy landscapes. Each replica is handled by a single thread making the parallelization straightforward. On the other hand, hard particles cannot overlap and do not contribute to the potential energy. In this case we carry out a pressure expansion of the isothermal-isobaric ensemble. Here we show how this expansion is able to resolve the phase diagrams of hard systems in two and three dimensions.

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