Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics

Abstract

Kinetically constrained lattice models of glasses introduced by Kob and Andersen (KA) are analyzed. It is proved that only two behaviors are possible on hypercubic lattices: either ergodicity at all densities or trivial non-ergodicity, depending on the constraint parameter and the dimensionality. But in the ergodic cases, the dynamics is shown to be intrinsically cooperative at high densities giving rise to glassy dynamics as observed in simulations. The cooperativity is characterized by two length scales whose behavior controls finite-size effects: these are essential for interpreting simulations. In contrast to hypercubic lattices, on Bethe lattices KA models undergo a dynamical (jamming) phase transition at a critical density: this is characterized by diverging time and length scales and a discontinuous jump in the long-time limit of the density autocorrelation function. By analyzing generalized Bethe lattices (with loops) that interpolate between hypercubic lattices and standard Bethe lattices, the crossover between the dynamical transition that exists on these lattices and its absence in the hypercubic lattice limit is explored. Contact with earlier results are made via analysis of the related Fredrickson-Andersen models, followed by brief discussions of universality, of other approaches to glass transitions, and of some issues relevant for experiments.

59 pages

References in corpus (11)

• Glassy dynamics of kinetically constrained models
• Coarse-grained microscopic model of glass formers
• Excitation lines and the breakdown of Stokes-Einstein relations in supercooled liquids
• Time and length scales in supercooled liquids
• Dynamic criticality in glass-forming liquids
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• Spatial structures and dynamics of kinetically constrained models for glasses
• Real space origin of temperature crossovers in supercooled liquids
• Finite size scaling analysis of the glass transition
• Clarification of the Bootstrap Percolation Paradox
• Dynamical arrest, tracer diffusion and Kinetically Constrained Lattice Gases

Cited by in corpus (27)

• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations
• Jamming Percolation and Glass Transitions in Lattice Models
• Corresponding States of Structural Glass Formers. II
• Space-time thermodynamics and subsystem observables in a kinetically constrained model of glassy systems
• Asymmetric exclusion processes with constrained dynamics
• Non-equilibrium dynamics of spin facilitated glass models
• On the study of force-balance percolation
• Tracking heterogeneous dynamics during the alpha-relaxation of a simple glass-former
• Finite-size effects for anisotropic bootstrap percolation: logarithmic corrections
• Bulk diffusion in a kinetically constrained lattice gas
• Bootstrap percolation and kinetically constrained models on hyperbolic lattices
• On the study of jamming percolation
• Critical phenomena in globally coupled excitable elements
• Dynamical heterogeneities in a two dimensional driven glassy model: current fluctuations and finite size effects
• Sharp threshold for the FA-2f kinetically constrained model
• Diffusive scaling of the Kob-Andersen model in ${\mathbb{Z}}^d$
• Vacancy diffusion in the triangular lattice dimer model
• A Multispin Algorithm for the Kob-Andersen Stochastic Dynamics on Regular Lattices
• Cooperative transport with selective kinetic constraints
• Theory of Kinetically-Constrained-Models Dynamics
• Jamming transition in kinetically constrained models with reflection symmetry
• Subdiffusive motion in kinetically constrained models
• Systematic perturbation approach for a dynamical scaling law in a kinetically constrained spin model
• Lattice Model of Glasses
• Anderson Localization on Husimi Trees and its implications for Many-Body localization
• Negative differential mobility of weakly driven particles in models of glass formers