Emergence of Long-range Correlations and Rigidity at the Dynamic Glass Transition

TL;DR

This paper demonstrates that the dynamic glass transition involves spontaneous symmetry breaking, leading to Goldstone modes and long-range correlations, and introduces a new way to calculate the glass shear modulus.

Contribution

It reveals the emergence of long-range correlations and Goldstone modes at the dynamic glass transition and provides a novel statistical mechanical expression for the shear modulus.

Findings

Long-range density correlations emerge at the glass transition.

Goldstone modes are associated with symmetry breaking.

A new expression for the glass shear modulus is derived.

Abstract

At the microscopic level, equilibrium liquid's translational symmetry is spontaneously broken at the so-called dynamic glass transition predicted by the mean-field replica approach. We show that this fact implies the emergence of Goldstone modes and long-range density correlations. We derive and evaluate a new statistical mechanical expression for the glass shear modulus.