Thermodynamic stability of hard sphere crystals in dimensions 3 through 10

TL;DR

This study investigates the thermodynamic stability of hard sphere crystals in dimensions 3 through 10, using simulations and free energy calculations, revealing that crystals remain stable up to at least 10 dimensions.

Contribution

It provides the first comprehensive analysis of high-dimensional hard sphere crystal stability, extending understanding beyond three dimensions and suggesting stability persists in higher dimensions.

Findings

Crystals are stable up to at least 10 dimensions.

Dimensional trends indicate stability likely beyond 10 dimensions.

Simulation-based estimates of crystal stability in high dimensions.

Abstract

Although much is known about the metastable liquid branch of hard spheres--from low dimension $d$ up to ${d\to\infty}$--its crystal counterpart remains largely unexplored for $d>3$. In particular, it is unclear whether the crystal phase is thermodynamically stable in high dimensions and thus whether a mean-field theory of crystals can ever be exact. In order to determine the stability range of hard sphere crystals, their equation of state is here estimated from numerical simulations, and fluid-crystal coexistence conditions are determined using a generalized Frenkel-Ladd scheme to compute absolute crystal free energies. The results show that the crystal phase is stable at least up to $d=10$, and the dimensional trends suggest that crystal stability likely persists well beyond that point.