Critical Dynamics in Glassy Systems

TL;DR

This paper links the critical dynamics of glassy systems to static properties by deriving scale-invariant equations from the structure of the replicated Gibbs free energy, highlighting the role of a key parameter ratio.

Contribution

It demonstrates that dynamical critical equations in glass models can be derived from static replicated free energy, connecting static and dynamic critical phenomena.

Findings

Critical dynamics are governed by a single parameter exponent.

The exponent parameter is expressed as a ratio of static six-point cumulants.

Derived equations apply to models described by mode coupling theory.

Abstract

Critical dynamics in various glass models including those described by mode coupling theory is described by scale-invariant dynamical equations with a single non-universal quantity, i.e. the so-called parameter exponent that determines all the dynamical critical exponents. We show that these equations follow from the structure of the static replicated Gibbs free energy near the critical point. In particular the exponent parameter is given by the ratio between two cubic proper vertexes that can be expressed as six-point cumulants measured in a purely static framework.