From Large Scale Rearrangements to Mode Coupling Phenomenology

Abstract

We consider the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs (Bethe lattices). Such models undergo a mean field glass transition upon increasing the graph connectivity or lowering the temperature. Focusing on the low temperature limit, we identify the large scale rearrangements responsible for the dynamical slowing-down near the transition. We are able to characterize exactly the dynamics near criticality by analyzing the statistical properties of such rearrangements. Our approach can be generalized to a large variety of glassy models on sparse random graphs, ranging from satisfiability to kinetically constrained models.

arXiv comment4 pages, 4 figures, minor corrections, accepted version

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• What do we learn from the shape of the dynamical susceptibility of glass-formers?
• Rigorous Inequalities between Length and Time Scales in Glassy Systems
• A Landscape Analysis of Constraint Satisfaction Problems
• On the dynamics of the glass transition on Bethe lattices
• Renormalization group analysis of the random first order transition
• Random subcubes as a toy model for constraint satisfaction problems
• Dynamic facilitation picture of a higher-order glass singularity
• Non-equilibrium dynamics of spin facilitated glass models
• Finitely coordinated models for low-temperature phases of amorphous systems
• From simple to complex networks: inherent structures, barriers and valleys in the context of spin glasses
• Statistical mechanics of error exponents for error-correcting codes
• Microscopic models of mode-coupling theory: the $F_{12}$ scenario
• Propagation of external regulation and asynchronous dynamics in random Boolean networks
• A simple one dimensional glassy Kac model
• Systematic perturbation approach for a dynamical scaling law in a kinetically constrained spin model