Quantitative field theory of the glass transition

TL;DR

This paper develops a microscopic replica field theory to analyze the dynamical transition in glasses, deriving critical exponents, correlation lengths, and validity criteria, with results consistent with simulations.

Contribution

It introduces a comprehensive microscopic replica field theory for the glass transition, providing analytical expressions for critical behavior and a Ginzburg criterion.

Findings

Derived mean field critical exponents

Analyzed critical behavior of four-point correlation functions

Established a Ginzburg criterion for the theory's validity

Abstract

We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we study analytically the critical behavior of a set of four-points correlation functions from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the Hypernetted Chain Approximation (HNC) for the Gibbs free energy and we find results that are consistent with numerical simulations.