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

Robert M. Turner, Robert L. Jack, Juan P. Garrahan

Research output: Contribution to journalArticle

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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 analyze 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, occurring at a coupling ε∗(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 sc(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.

Original languageEnglish
Article number022115
JournalPhysical Review E
Volume92
Issue number2
DOIs
Publication statusPublished - 10 Aug 2015

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Spin Models
Glass Transition
Replica
Overlap
Phase Transition
Thermodynamics
glass
replicas
Triangular
Square-based pyramid
Vanish
Path Sampling
Dynamical Transition
Coupled Maps
Metastable States
Model
Three-dimension
Counting
thermodynamics
Space-time

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Overlap and activity glass transitions in plaquette spin models with hierarchical dynamics. / Turner, Robert M.; Jack, Robert L.; Garrahan, Juan P.

In: Physical Review E, Vol. 92, No. 2, 022115, 10.08.2015.

Research output: Contribution to journalArticle

Turner, Robert M. ; Jack, Robert L. ; Garrahan, Juan P. / Overlap and activity glass transitions in plaquette spin models with hierarchical dynamics. In: Physical Review E. 2015 ; Vol. 92, No. 2.
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