Free minimization of the fundamental measure theory functional: Freezing of parallel hard squares and cubes

Due to remarkable advances in colloid synthesis techniques, systems of squares and cubes, once an academic abstraction for theorists and simulators, are nowadays an experimental reality. By means of a free minimization of the free-energy functional, we apply fundamental measure theory to analyze the phase behavior of parallel hard squares and hard cubes. We compare our results with those obtained by the traditional approach based on the Gaussian parameterization, finding small deviations and good overall agreement between the two methods. For hard squares, our predictions feature at intermediate packing fraction a smectic phase, which is however expected to be unstable due to thermal fluctuations. Due to this inconsistency, we cannot determine unambiguously the prediction of the theory for the expected fluid-to-crystal transition of parallel hard squares, but we deduce two alternative scenarios: (i) a second-order transition with a coexisting vacancy-rich crystal or (ii) a higher-density first-order transition with a coexisting crystal characterized by a lower vacancy concentration. In accordance with previous studies, a second-order transition with a high vacancy concentration is predicted for hard cubes.