Towards a Theory of the Glass Crossover

TL;DR

This paper applies a field-theoretical approach to Mode-Coupling Theory, revealing that fluctuations transform the glass transition singularity into a crossover to activated dynamics, advancing understanding of glassy systems.

Contribution

It introduces a dynamical field-theoretical framework for MCT, showing fluctuations lead to a stochastic equation that explains the crossover from singularity to activated dynamics.

Findings

Leading contributions match a stochastic glassy equation.

Fluctuations turn the MCT singularity into a dynamical crossover.

The approach provides a new perspective on the glass transition mechanism.

Abstract

The standard field-theoretical procedure to study the effect of long wavelength fluctuations on a genuine second-order phase transition is applied to the Mode-Coupling-Theory (MCT) dynamical singularity at $T_c$ in the $\beta$ regime. Technically this is achieved by a dynamical field-theoretical decoration of MCT that can be studied by a loop expansion. An explicit computation shows that at all orders the leading contributions are the same of a dynamical stochastic glassy equation, {\it i.e} an extension of the standard MCT equation for the critical correlator with local random fluctuations of the separation parameter. It is suggested that the equation is an essential ingredient in the process that turns the singularity at $T_c$ into a dynamical crossover to activated dynamics.