Glass transition and random close packing above three dimensions

TL;DR

This study investigates dense hard spheres in dimensions 3 to 12, revealing discrepancies between static and dynamic theories of glasses and providing new estimates for random close packing densities in high dimensions.

Contribution

It offers numerical evidence supporting static replica theory over dynamic mode-coupling theory in high-dimensional glass behavior and estimates random close packing densities in large dimensions.

Findings

Results align with static replica theory

Disagree with dynamic mode-coupling theory

Provides new estimates for packing densities in high dimensions

Abstract

Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static replica theory, but disagree with the dynamic mode-coupling theory, indicating that key ingredients of high-dimensional physics are missing from the latter. We also obtain numerical estimates of the random close packing density, which provides new insights into the mathematical problem of packing spheres in large dimension.