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

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.

References in corpus (8)

• Irreversible reorganization in a supercooled liquid originates from localised soft modes
• Finite size scaling for the core of large random hypergraphs
• Fluctuations in glassy systems
• Dynamic facilitation picture of a higher-order glass singularity
• Predictive power of MCT: Numerics and Finite size scaling for a mean field spin glass
• Kovacs effect in facilitated spin models of strong and fragile glasses
• Cooperative heterogeneous facilitation: multiple glassy states and glass-glass transition
• Microscopic models of mode-coupling theory: the $F_{12}$ scenario

Cited by in corpus (9)

• Can the glass transition be explained without a growing static length scale?
• Solvable Models of Supercooled Liquids in Three Dimensions
• Random-Field Ising like effective theory of the glass transition: I Mean-Field Models
• The fate of the bootstrap percolation hybrid critical point in finite dimension
• Scaling and universality in glass transition
• Crossover from $\beta$- to $\alpha$-relaxation in cooperative facilitation dynamics
• The Random-Diluted Triangular Plaquette Model: study of phase transitions in a Kinetically Constrained Model
• Thermodynamics of the Fredrickson-Andersen Model on the Bethe Lattice
• Theory of Kinetically-Constrained-Models Dynamics