Static and dynamic lengthscales in a simple glassy plaquette model

Abstract

We study static and dynamic spatial correlations in a two-dimensional spin model with four-body plaquette interactions and standard Glauber dynamics by means of analytic arguments and Monte Carlo simulations. We study in detail the dynamical behaviour which becomes glassy at low temperatures due to the emergence of effective kinetic constraints in a dual representation where spins are mapped to plaquette variables. We study the interplay between non-trivial static correlations of the spins and the dynamic `four-point' correlations usually studied in the context of supercooled liquids. We show that slow dynamics is spatially heterogeneous due to the presence of diverging lengthscales and scaling, as is also found in kinetically constrained models. This analogy is illustrated by a comparative study of a froth model where the kinetic constraints are imposed.

12 pages, 13 figs; published version

References in corpus (5)

• Glassy dynamics of kinetically constrained models
• On the Adam-Gibbs-Wolynes scenario for the viscosity increase in glasses
• Renormalization group study of a kinetically constrained model for strong glasses
• Glassy behaviour in an exactly solved spin system with a ferromagnetic transition
• A few bubbles in a glass

Cited by in corpus (29)

• Theoretical perspective on the glass transition and amorphous materials
• The frustration-based approach of supercooled liquids and the glass transition: a review and critical assessment
• Perspective: Configurational entropy of glass-forming liquids
• Fractal Symmetric Phases of Matter
• Heterogeneity and growing lengthscales in the dynamics of kinetically constrained lattice gases in two dimensions
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography
• Caging and mosaic lengthscales in plaquette spin models of glasses
• Spin slush in an extended spin ice model
• Fluctuations in glassy systems
• Random pinning in glassy spin models with plaquette interactions
• Fluctuations in the coarsening dynamics of the O(N) model: are they similar to those in glassy systems?
• The melting of stable glasses is governed by nucleation-and-growth dynamics
• Non-equilibrium dynamics of spin facilitated glass models
• Growing dynamical length, scaling and heterogeneities in the 3d Edwards-Anderson model
• Patch-repetition correlation length in glassy systems
• Artificial spin ice and vertex models
• Fluctuation-dissipation relations in plaquette spin systems with multi-stage relaxation
• Dynamic Heterogeneity in the Glauber-Ising chain
• Role of fluctuations in the phase transitions of coupled plaquette spin models of glasses
• On the relation between kinetically constrained models of glass dynamics and the random first-order transition theory
• Exact solutions to plaquette Ising models with free and periodic boundaries
• Fracton excitations in classical frustrated kagome spin models
• Defect-Mediated Relaxation in the Random Tiling Phase of a Binary Mixture: Birth, Death and Mobility of an Atomic Zipper
• The Random-Diluted Triangular Plaquette Model: study of phase transitions in a Kinetically Constrained Model
• Mixing length scales of low temperature spin plaquettes models
• Nonlinear dielectric response in glasses: restoring forces and avoided spin-glass criticality
• Subdiffusive motion in kinetically constrained models
• Stretched exponentials and tensionless glass in the plaquette Ising model
• Finding ground states of a square Newman-Moore lattice with sides equal to a Mersenne number using the Rule 60 cellular automaton