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

Silvio Franz ¹, Mauro Sellitto ²

Journal of Statistical Mechanics (2013) P02025

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.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
  CNRS : UMR8626 – Université Paris XI – Paris Sud
• 2 : Laboratoire de Physique de l’ENS Lyon (Phys-ENS)
  CNRS : UMR5672 – École Normale Supérieure (ENS) – Lyon