Long-wavelength fluctuations lead to a model of the glass crossover

TL;DR

This paper develops a field-theoretical model incorporating long-wavelength fluctuations to explain the crossover from MCT-predicted dynamical singularity to realistic glassy dynamics, highlighting the role of dynamical heterogeneities.

Contribution

It introduces a resummed perturbative approach extending MCT with local random fluctuations, providing a unified explanation for the glass crossover and emergent dynamical heterogeneities.

Findings

MCT singularity is replaced by a crossover due to fluctuations.

Dynamical heterogeneities naturally arise as ergodicity-restoring mechanisms.

The model quantitatively matches experimental observations of glassy dynamics.

Abstract

The effect of long wavelength fluctuations on the Mode-Coupling-Theory (MCT) dynamical singularity at $T_c$ in the $\beta$ regime is studied by means of the standard field-theoretical procedure for a genuine second-order phase transition. The resulting perturbative loop expansion can be resummed leading to an extension of the MCT equation for the critical correlator with local random fluctuations of the separation parameter. The corresponding model explains both qualitatively and quantitatively why the MCT dynamical singularity is transformed into a crossover from relaxational to activated dynamics. Dynamical Heterogeneities emerge naturally as the ergodicity-restoring mechanism instead of {\it ad hoc} hopping processes.