Role of fluctuations in the phase transitions of coupled plaquette spin models of glasses

Abstract

We study the role of fluctuations on the thermodynamic glassy properties of plaquette spin models, more specifically on the transition involving an overlap order parameter in the presence of an attractive coupling between different replicas of the system. We consider both short-range fluctuations associated with the local environment on Bethe lattices and long-range fluctuations that distinguish Euclidean from Bethe lattices with the same local environment. We find that the phase diagram in the temperature-coupling plane is very sensitive to the former but, at least for the $3$-dimensional (square pyramid) model, appears qualitatively or semi-quantitatively unchanged by the latter. This surprising result suggests that the mean-field theory of glasses provides a reasonable account of the glassy thermodynamics of models otherwise described in terms of the kinetically constrained motion of localized defects and taken as a paradigm for the theory of dynamic facilitation. We discuss the possible implications for the dynamical behavior.

23 pages, 6 figures

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• Glassy dynamics of kinetically constrained models
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• Caging and mosaic lengthscales in plaquette spin models of glasses
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• Random Field Ising-like effective theory of the glass transition II: Finite Dimensional Models
• Statistical mechanics of coupled supercooled liquids in finite dimensions
• Random-Field Ising like effective theory of the glass transition: I Mean-Field Models
• On the overlap between configurations in glassy liquids
• Beyond the Freshman's Dream: Classical fractal spin liquids from matrix cellular automata in three-dimensional lattice models