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

TL;DR

This paper investigates thermodynamic and dynamic phase transitions in plaquette spin models of glasses, revealing overlap and activity transitions that vanish at low temperatures, and introduces a 3D model to extend these findings.

Contribution

It maps coupled-replica systems to single replicas in a magnetic field and analyzes phase transitions, including a new 3D square pyramid model with similar behaviors.

Findings

Coupled-replica system shows a phase transition at a coupling epsilon*(T) that vanishes at low T.

Single TPM exhibits space-time dynamical transitions between active and inactive phases.

The 3D square pyramid model also displays overlap and activity transitions.

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.