Overlap and activity glass transitions in plaquette spin models with hierarchical dynamics

Abstract

We consider thermodynamic and dynamic phase transitions in plaquette spin models of glasses. The thermodynamic transitions involve coupled (annealed) replicas of the model. We map these coupled-replica systems to a single replica in a magnetic field, which allows us to analyse the resulting phase transitions in detail. For the triangular plaquette model (TPM), we find for the coupled-replica system a phase transition between high- and low-overlap phases, occuring at a coupling eps*(T), which vanishes in the low-temperature limit. Using computational path sampling techniques, we show that a single TPM also displays space-time transitions between active and inactive dynamical phases. These first-order dynamical transitions occur at a critical counting field s_c(T)>=0 that appears to vanish at zero temperature, in a manner reminiscent of the thermodynamic overlap transition. In order to extend the ideas to three dimensions we introduce the square pyramid model which also displays both overlap and activity transitions. We discuss a possible common origin of these various phase transitions, based on long-lived (metastable) glassy states.

12 pages, 9 figs

References in corpus (12)

• Theoretical perspective on the glass transition and amorphous materials
• The large deviation approach to statistical mechanics
• Supercooled Liquids for Pedestrians
• Glassy dynamics of kinetically constrained models
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Fluctuations and response of nonequilibrium states
• Finite-temperature critical point of a glass transition
• Evidence for a disordered critical point in a glass-forming liquid
• Caging and mosaic lengthscales in plaquette spin models of glasses
• Equivalence of matrix product ensembles of trajectories in open quantum systems
• Gonihedric (and Fuki-Nuke) Order
• On the relation between kinetically constrained models of glass dynamics and the random first-order transition theory

Cited by in corpus (19)

• Fractal Symmetric Phases of Matter
• Quantum East model: localization, non-thermal eigenstates and slow dynamics
• Phase transition for quenched coupled replicas in a plaquette spin model of glasses
• The melting of stable glasses is governed by nucleation-and-growth dynamics
• Trajectory phase transitions in non-interacting spin systems
• Statistical mechanics of coupled supercooled liquids in finite dimensions
• Artificial spin ice and vertex models
• Random-Field Ising like effective theory of the glass transition: I Mean-Field Models
• Structure of inactive states of a binary Lennard-Jones mixture
• Role of fluctuations in the phase transitions of coupled plaquette spin models of glasses
• Beyond the Freshman's Dream: Classical fractal spin liquids from matrix cellular automata in three-dimensional lattice models
• Dynamical Facilitation Governs the Equilibration Dynamics of Glasses
• Boundary conditions dependence of the phase transition in the quantum Newman-Moore model
• Mean-field phase diagram and spin glass phase of the dipolar Kagome Ising antiferromagnet
• Dynamical phase transitions for the activity biased Ising model in a magnetic field
• Synchronization transition in the double dimer model on the cubic lattice
• The Random-Diluted Triangular Plaquette Model: study of phase transitions in a Kinetically Constrained Model
• Dynamical phase transition in the activity-biased fully-connected random field Ising model: connection with glass-forming systems
• Dynamical Phase Transitions and their Relation to Thermodynamic Glass Physics