Thermodynamic stability of the cubatic phase of hard cut spheres evaluated by expanded ensemble simulations

The system of hard cut spheres (disk-shaped particles formed by symmetrically truncating the end caps of a sphere) exhibits an intriguing cubatic phase with cubic orientational symmetry. However, it is unclear whether this phase is metastable with respect to the columnar phase. We attempt to provide an answer to this question by carrying out free energy calculations by the expanded ensemble Monte Carlo method. We conclude that there may be a very small region of cubatic stability in the vicinity of the isotropic-cubatic phase transition, but that that transition would need to be determined more accurately to obtain a definitive answer. We also comment on the efficacy of the expanded ensemble method for these kinds of calculations.