Renormalization group analysis of the random first order transition

TL;DR

This paper applies a real-space renormalization group analysis to the replica free-energy functional of glass-forming liquids, revealing a finite-dimensional ideal glass transition with properties limited by a diverging length scale.

Contribution

It introduces a real-space RG approach to analyze the glass transition beyond mean-field, highlighting the role of a diverging length scale in metastable states.

Findings

Finite-dimensional ideal glass transition similar to mean-field.

Metastable state properties are limited by a diverging length scale.

Critical exponents match those of a first-order transition.

Abstract

We consider the approach describing glass formation in liquids as a progressive trapping in an exponentially large number of metastable states. To go beyond the mean-field setting, we provide a real-space renormalization group (RG) analysis of the associated replica free-energy functional. The present approximation yields in finite dimensions an ideal glass transition similar to that found in mean field. However, we find that along the RG flow the properties associated with metastable glassy states, such as the configurational entropy, are only defined up to a characteristic length scale that diverges as one approaches the ideal glass transition. The critical exponents characterizing the vicinity of the transition are the usual ones associated with a first-order discontinuity fixed point.