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 33-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.
Highlights
This work is an assessment of the role of the fluctuations on overlap-based phase transitions in plaquette spin models of glasses in the presence of a biasing field
At least for the 3-dimensional square pyramid model (SPyM) and when comparing with recent simulation results in Euclidean space [12], the mean-field description, provided it correctly encompasses the description of the local environment, appears surprisingly robust with respect to long-range fluctuations
The T − ε phase diagram is informative but the most relevant aspect for glassy physics is the behavior for ε = 0
Summary
The plaquette spin models (PSM) [1,2,3,4,5,6] provide an interesting testing ground for theories of the glass transition. The location of the terminal critical point(s) is at higher temperature and higher coupling and the associated critical exponents are different, due to the absence of long-range fluctuations; as sketched, one expects that these fluctuations will enforce convexity of the thermodynamic potential V (q) (the free-energy cost for maintaining an overlap q with a reference configuration [14, 28]), preventing true metastability All this is akin to what is obtained in a conventional 3-dimensional ferromagnet at a first-order phase transition and does not call into question the qualitative or even semi-quantitative relevance of the mean-field description.
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