Microscopic models of mode-coupling theory: the $F_{12}$ scenario

Abstract

We provide extended evidence that mode-coupling theory (MCT) of supercooled liquids for the ${\mathsf{F}}_{12}$ schematic model admits a microscopic realization based on facilitated spin models with tunable facilitation. Depending on the facilitation strength, one observes two distinct dynamic glass transition lines--continuous and discontinuous--merging at a dynamical tricritical-like point with critical decay exponents consistently related by MCT predictions. The mechanisms of dynamical arrest can be naturally interpreted in geometrical terms: the discontinuous and continuous transitions correspond to bootstrap and standard percolation processes, in which the incipient spanning cluster of frozen spins forms either a compact or a fractal structure, respectively. Our cooperative dynamic facilitation picture of glassy behavior is complementary to the one based on disordered systems and can account for higher-order singularity scenarios in the absence of a finite temperature thermodynamic glass transition. We briefly comment on the relevance of our results to finite spatial dimensions and to the ${\mathsf{F}}_{13}$ schematic model.

Final, published version

References in corpus (36)

• Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function
• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Energy flow, partial equilibration and effective temperatures in systems with slow dynamics
• Glassy dynamics of kinetically constrained models
• k-core organization of complex networks
• Scaling behavior in the $\beta$-relaxation regime of a supercooled Lennard-Jones mixture
• Colloidal Gels: Equilibrium and Non-Equilibrium Routes
• Dynamics on the Way to Forming Glass: Bubbles in Space-time
• On the Out of Equilibrium Relaxation of the Sherrington - Kirkpatrick model
• Higher order glass-transition singularities in colloidal systems with attractive interactions
• Reentrant glass transition in a colloid-polymer mixture with depletion attractions
• Mode-Coupling Theory (MCT) Lecture Notes
• The effective temperature
• Mode-Coupling Approximations, Glass Theory and Disordered Systems
• Bootstrap Percolation on Complex Networks
• A first principle computation of the thermodynamics of glasses
• Jamming Percolation and Glass Transitions in Lattice Models
• Field Theory of Fluctuations in Glasses
• On the dynamics of the glass transition on Bethe lattices
• Facilitated spin models on Bethe lattice: bootstrap percolation, mode-coupling transition and glassy dynamics
• Mode-coupling theory for the slow collective dynamics of fluids adsorbed in disordered porous media
• Cooperativity Beyond Caging: Generalized Mode Coupling Theory
• On Mean Field Glassy Dynamics out of Equilibrium
• Aging in lattice-gas models with constrained dynamics
• Tricritical point in heterogeneous k-core percolation
• On the critical slowing down exponents of mode coupling theory
• Mode-Coupling as a Landau Theory of the Glass Transition
• From Large Scale Rearrangements to Mode Coupling Phenomenology
• Dynamics in a supercooled liquid of symmetric dumbbells: Reorientational hopping for small molecular elongations
• Free-volume kinetic models of granular matter
• Dynamic arrest of colloids in porous environments: disentangling crowding and confinement
• Dynamic facilitation picture of a higher-order glass singularity
• Aging dynamics and density relaxation in granular compaction
• Comment on ``Jamming Percolation and Glass Transitions in Lattice Models.''
• On the relation between kinetically constrained models of glass dynamics and the random first-order transition theory
• Comment on "Mode-Coupling Theory as a Mean-Field Description of the Glass Transition"

Cited by in corpus (13)

• Critical phenomena in heterogeneous k-core percolation
• Cooperative heterogeneous facilitation: multiple glassy states and glass-glass transition
• Scaling and universality in glass transition
• Crossover from $\beta$- to $\alpha$-relaxation in cooperative facilitation dynamics
• Disconnected glass-glass transitions and swallowtail bifurcations in microscopic spin models with facilitated dynamics
• Finite-size critical fluctuations in microscopic models of mode-coupling theory
• The Fredrickson-Andersen model with random pinning on Bethe lattices and its MCT transitions
• Percolation approach to glassy dynamics with continuously broken ergodicity
• Fredrickson-Andersen model on Bethe lattice with random pinning
• Cluster structure and dynamics in gels and glasses
• Theory of Kinetically-Constrained-Models Dynamics
• Logarithmic critical slowing down in complex systems: from statics to dynamics
• Nonequilibrium Phase Transition in Constrained Adsorption