On the absence of the glass transition in two dimensional hard disks

TL;DR

This paper investigates the absence of a true glass transition in two-dimensional hard disks, suggesting that the transition predicted by mean-field theory is smeared out in two dimensions, aligning with recent findings.

Contribution

It provides a systematic analysis indicating the non-existence of a sharp glass transition in two dimensions, extending the understanding of the lower critical dimension for the ideal glass transition.

Findings

Mean-field predicts an ideal glass transition in 2D hard disks.

Systematic expansion suggests the transition is smeared out in 2D.

Results align with recent studies indicating no true glass transition in 2D.

Abstract

In this paper we study the glass transition in a model of identical hard spheres, focusing on the two dimensional case. In the mean-field limit the model exhibits an ideal glass transition of the same nature of that found in discontinuous spin glasses. Nevertheless, a systematic expansion around the mean-field solution seems to indicate that the glass transitions is smeared out in two dimensions, in agreement with some recent results. Our investigation could be generalized to higher spatial dimensions, providing a way to determine the lower critical dimensionality of the mean-field ideal glass picture.