Field Theory of Fluctuations in Glasses

TL;DR

This paper presents a field-theoretical framework for understanding fluctuations and dynamical heterogeneities in supercooled liquids near the MCT singularity, linking them to a cubic field theory with random fields.

Contribution

It introduces a novel field-theoretical approach that characterizes fluctuations in supercooled liquids, highlighting the role of self-induced disorder and deriving an upper critical dimension of 8.

Findings

Heterogeneities are linked to variations in initial conditions.

The theory predicts a cubic field model with random field effects.

Numerical simulations support the finite size scaling predictions.

Abstract

We develop a field-theoretical description of dynamical heterogeneities and fluctuations in supercooled liquids close to the (avoided) MCT singularity. Using quasi-equilibrium arguments we eliminate time from the description and we completely characterize fluctuations in the beta regime. We identify different sources of fluctuations and show that the most relevant ones are associated to variations of "self-induced disorder" in the initial condition of the dynamics. It follows that heterogeneites can be describes through a cubic field theory with an effective random field term. The phenomenon of perturbative dimensional reduction ensues, well known in random field problems, which implies an upper critical dimension of the theory equal to 8. We apply our theory to finite size scaling for mean-field systems and we test its prediction against numerical simulations.