Dimensional crossover of the fundamental-measure functional for parallel hard cubes

TL;DR

This paper introduces a regularized fundamental-measure functional for parallel hard cubes that correctly transitions across dimensions, enabling the study of complex phases and extending to models like parallelepipeds and cylinders.

Contribution

It develops a regularized functional with proper dimensional crossovers for parallel hard cubes and extends the approach to parallelepipeds and cylinders, facilitating studies of inhomogeneous phases.

Findings

Functional has correct dimensional crossovers

Extension to parallelepipeds and cylinders demonstrated

Framework for inhomogeneous phase analysis established

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 right dimensional crossovers to any smaller dimension, thus allowing to use it 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. The multicomponent version of the latter system is also given, and it is suggested how to reformulate it as a restricted-orientation model for liquid crystals. Finally, the method is further extended to build a functional for a mixture of parallel hard cylinders.