Statistical Mechanics of the Glass Transition

TL;DR

This paper develops a statistical mechanics framework for 2D glass-forming systems using Voronoi tessellation, explaining key glass transition phenomena and identifying two distinct transition temperatures without free parameters.

Contribution

It introduces a novel Voronoi-based statistical mechanics approach that explains glass transition phenomenology in 2D systems without free parameters.

Findings

Identification of two distinct transition temperatures, T_g and T_k.

Explanation of glass transition phenomenology.

Correlation of T_g with jamming and T_k with quasi-crystal formation.

Abstract

The statistical mechanics of simple glass forming systems in 2 dimensions is worked out. The glass disorder is encoded via a Voronoi tessellation, and the statistical mechanics is performed directly in this encoding. The theory provides, without free parameters, an explanation of the glass transition phenomenology, including the identification of two different temperatures, $T_g$ and $T_k$, the first associated with jamming and the second associated with the appearance of a quasi-crystal at very low temperatures.