Free Minimization of the Fundamental Measure Theory Functional: Freezing of Parallel Hard Squares and Cubes

TL;DR

This paper applies Fundamental Measure Theory with free energy minimization to analyze phase transitions in parallel hard squares and cubes, comparing results with traditional Gaussian methods and predicting specific phase behaviors.

Contribution

It introduces a free minimization approach to Fundamental Measure Theory for studying phase behavior of hard squares and cubes, providing new insights and comparisons with existing methods.

Findings

Good agreement with Gaussian parameterization results

Prediction of smectic phase for hard squares at intermediate density

Identification of phase transition types for squares and cubes

Abstract

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. This implies that for hard squares the theory predicts either a vacancy-rich second-order transition or a vacancy-poor weakly first-order phase transition at higher density. In accordance with previous studies, a second-order transition with a high vacancy concentration is predicted for hard cubes.