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

TL;DR

This paper investigates how fluctuations influence the thermodynamic properties of plaquette spin models of glasses, revealing that local fluctuations significantly affect the phase diagram, while long-range fluctuations have limited impact.

Contribution

It demonstrates that mean-field theory remains a good approximation for glassy thermodynamics despite local fluctuations, challenging previous assumptions about the importance of long-range fluctuations.

Findings

Local fluctuations strongly affect the phase diagram.

Long-range fluctuations have minimal impact on the phase diagram.

Mean-field theory effectively describes glassy thermodynamics in these models.

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.