Dimensional Crossover of the Fundamental-Measure Functional for Parallel Hard Cubes

Abstract

We present a regularization of the recently proposed fundamental-measure functional for a mixture of parallel hard cubes. The regularized functional is shown to have correct dimensional crossovers to any smaller dimension, thus allowing its use to study highly inhomogeneous phases (such as the solid phase). Furthermore, it is shown how the functional of the slightly more-general model of parallel hard parallelepipeds can be obtained using the zero-dimensional functional as a generating functional. Extensions to the multicomponent system, a restricted-orientation model, and mixtures or prallel hard cylinders are also given.