The Glass Crossover from Mean-Field Spin-Glasses to Supercooled Liquids

TL;DR

This paper explores the connection between spin-glass models and supercooled liquids through a dynamical Landau theory, highlighting finite-size effects and the glass crossover described by Stochastic-Beta-Relaxation.

Contribution

It establishes a rigorous link between spin-glass and supercooled liquid dynamics using Landau theory, clarifying the glass crossover without requiring statistical field theory expertise.

Findings

Finite-size corrections in mean-field models analyzed

Loop corrections in finite-dimensional models discussed

Landau theory applied to Mode-Coupling-Theory for supercooled liquids

Abstract

Stochastic-Beta-Relaxation (SBR) provides a characterisation of the glass crossover in discontinuous Spin-Glasses and Supercoooled liquid. Notably it can be derived through a rigorous computation from a dynamical Landau theory. In this paper I will discuss the precise meaning of this connection in a language that does not require familiarity with statistical field theory. I will discuss finite-size corrections in mean-field Spin-Glass models and loop corrections in finite-dimensional models that are both described by the dynamical Landau theory considered. Then I will argue that the same Landau theory can be associated to supercooled liquid described by Mode-Coupling-Theory invoking a physical principle of time-scale invariance.