Critical fluctuations and breakdown of Stokes-Einstein relation in the Mode-Coupling Theory of glasses

TL;DR

This paper explains the breakdown of the Stokes-Einstein relation in glassy systems using mode-coupling theory, highlighting critical fluctuations and the role of a diverging length scale at the transition.

Contribution

It introduces a critical fluctuation-based explanation for the Stokes-Einstein breakdown within MCT, and identifies the upper critical dimension as d_c=8.

Findings

Critical fluctuations explain the Stokes-Einstein breakdown.

MCT transition acts as a critical point with a diverging length scale.

Upper critical dimension of MCT is d_c=8.

Abstract

We argue that the critical dynamical fluctuations predicted by the mode-coupling theory (MCT) of glasses provide a natural mechanism to explain the breakdown of the Stokes-Einstein relation. This breakdown, observed numerically and experimentally in a region where MCT should hold, is one of the major difficulty of the theory, for which we propose a natural resolution based on the recent interpretation of the MCT transition as a bona fide critical point with a diverging length scale. We also show that the upper critical dimension of MCT is d_c=8.