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

TL;DR

This paper introduces an expanded isothermal-isobaric [N]pT Monte Carlo method to accurately simulate cluster-crystal forming penetrable sphere models, resolving previous ambiguities in phase behavior at different temperatures.

Contribution

The authors develop a novel [N]pT ensemble simulation approach that allows for fluctuating particle number and lattice spacing, enabling detailed phase diagram analysis of cluster crystals.

Findings

Equilibrium occupancy increases linearly at high temperatures and densities.

At low temperatures, occupancy plateaus at integer values, with continuous density dependence.

The method resolves the ambiguous crossover around T~0.1.

Abstract

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 $n_{\mathrm{c}}^{\mathrm{eq}}$ of face-centered cubic (FCC) crystal increases linearly. At low temperatures, although $n_{\mathrm{c}}^{\mathrm{eq}}$ plateaus at integer values, the crystal behavior changes continuously with density. The previously ambiguous crossover around $T\sim0.1$ is resolved.