Mode-Coupling as a Landau Theory of the Glass Transition

TL;DR

This paper presents a derivation of Mode Coupling Theory (MCT) as a Landau theory, revealing the universal aspects of the glass transition and analyzing corrections to the standard equations.

Contribution

It formulates MCT as a Landau theory based on an expansion of dynamical equations, highlighting the universality of key predictions despite higher order corrections.

Findings

The square root singularity of the order parameter is universal.

The scaling function in the eta regime remains unchanged.

The relation between eta and au exponents is preserved.

Abstract

We derive the Mode Coupling Theory (MCT) of the glass transition as a Landau theory, formulated as an expansion of the exact dynamical equations in the difference between the correlation function and its plateau value. This sheds light on the universality of MCT predictions. While our expansion generates higher order non-local corrections that modify the standard MCT equations, we find that the square root singularity of the order parameter, the scaling function in the \beta regime and the functional relation between the exponents defining the \alpha and \beta timescales are universal and left intact by these corrections.