A percolation model for slow dynamics in glass-forming materials

TL;DR

This paper proposes a percolation-based model linking the glass transition to the critical behavior of mobile regions in configuration space, explaining slow dynamics and relaxation phenomena in glass-forming materials.

Contribution

It introduces a novel percolation model that captures key glassy dynamics and predicts the range of stretching exponents and their dependence on physical parameters.

Findings

Predicts stretching exponents between 1/3 and 1.

Shows divergence of structural relaxation time near the transition.

Provides functional relationships between relaxation time, exponent, and control parameters.

Abstract

We identify a link between the glass transition and percolation of mobile regions in configuration space. We find that many hallmarks of glassy dynamics, for example stretched-exponential response functions and a diverging structural relaxation time, are consequences of the critical properties of mean-field percolation. Specific predictions of the percolation model include the range of possible stretching exponents $1/3 \leq \beta \leq 1$ and the functional dependence of the structural relaxation time $\tau_\alpha$ and exponent $\beta$ on temperature, density, and wave number.