[N]pT Monte Carlo Simulations of the Cluster-Crystal-Forming Penetrable Sphere Model

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Certain models with purely repulsive pair interactions can form cluster crystals with multiply-occupied lattice sites. Simulating these models' equilibrium properties is, however, quite challenging. Here, we develop an expanded isothermal-isobaric [N]pT ensemble that surmounts this problem by allowing both particle number and lattice spacing to fluctuate. We apply the method with a Monte Carlo simulation scheme to solve the phase diagram of a prototypical cluster-crystal former, the penetrable sphere model (PSM), and compare the results with earlier theoretical predictions. At high temperatures and densities, the equilibrium occupancy nceq of face-centered cubic (FCC) crystal increases linearly. At low temperatures, although nceq plateaus at integer values, the crystal behavior changes continuously with density. The previously ambiguous crossover around T 0.1 is resolved.