Statics and dynamics of infinite-dimensional liquids and glasses: a parallel, compact derivation

TL;DR

This paper presents a concise derivation of static and dynamic equations for infinite-dimensional liquids and glasses, linking static replica methods with dynamic supersymmetric formulations within the mean field glass transition framework.

Contribution

It introduces a unified, compact derivation of static and dynamic equations for infinite-dimensional systems, connecting replica and supersymmetric approaches.

Findings

Static and dynamic results are consistent.

Supports the Random First Order Transition scenario.

Provides a unified derivation framework.

Abstract

We provide a compact derivation of the static and dynamic equations for infinite-dimensional particle systems in the liquid and glass phases. The static derivation is based on the introduction of an "auxiliary" disorder and the use of the replica method. The dynamic derivation is based on the general analogy between replicas and the supersymmetric formulation of dynamics. We show that static and dynamic results are consistent, and follow the Random First Order Transition scenario of mean field disordered glassy systems.