Finite-size critical fluctuations in microscopic models of mode-coupling theory

TL;DR

This paper investigates finite-size critical fluctuations in microscopic facilitated spin models related to mode-coupling theory, comparing numerical results with theoretical predictions to understand dynamical heterogeneity near the glass transition.

Contribution

It demonstrates that the field theoretical description accurately predicts fluctuation behavior in facilitated spin models, identifying the persistence function as the key order parameter.

Findings

Theoretical predictions match numerical data when using the persistence function.

Finite-size scaling of fluctuations aligns with quasi-equilibrium field theory.

Critical fluctuations are well-characterized in the beta relaxation regime.

Abstract

Facilitated spin models on random graphs provide an ideal microscopic realization of the mode-coupling theory of supercooled liquids: they undergo a purely dynamic glass transition with no thermodynamic singularity. In this paper we study the fluctuations of dynamical heterogeneity and their finite-size scaling properties in the beta relaxation regime of such microscopic spin models. We compare the critical fluctuations behavior for two distinct measures of correlations with the results of a recently proposed field theoretical description based on quasi-equilibrium ideas. We find that the theoretical predictions perfectly fit the numerical simulation data once the relevant order parameter is identified with the persistence function of the spins.