Glasses and replicas

TL;DR

This paper reviews a first-principles replica formalism for understanding glass properties, applicable to systems with and without quenched disorder, and capable of analytically deriving key glass transition behaviors.

Contribution

It introduces a unified replica approach that applies to both dynamic and equilibrium transitions in glasses, including systems without quenched disorder.

Findings

Analytic computations align with numerical simulations.

The method describes behavior near both dynamic and Kauzmann transitions.

Applicable to simple mean field models and realistic glass systems.

Abstract

We review the approach to glasses based on the replica formalism. The replica approach presented here is a first principle's approach which aims at deriving the main glass properties from the microscopic Hamiltonian. In contrast to the old use of replicas in the theory of disordered systems, this replica approach applies also to systems without quenched disorder (in this sense, replicas have nothing to do with computing the average of a logarithm of the partition function). It has the advantage of describing in an unified setting both the behaviour near the dynamic transition (mode coupling transition) and the behaviour near the equilibrium `transition' (Kauzmann transition) that is present in fragile glasses. The replica method may be used to solve simple mean field models, providing explicit examples of systems that may be studied analytically in great details and behave similarly to the experiments. Finally, using the replica formalism and some well adapted approximation schemes, it is possible to do explicit analytic computations of the properties of realistic models of glasses. The results of these first-principle computations are in reasonable agreement with numerical simulations. Draft of a chapter prepared for the book "Structural Glasses and Supercooled Liquids: Theory, Experiment, and Applications."