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Mixing length scales of low temperature spin plaquettes models
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Chleboun, P., Faggionato, A., Martinelli, F. and Toninelli, C. (2017) Mixing length scales of low temperature spin plaquettes models. Journal of Statistical Physics, 169 (3). pp. 441-471. doi:10.1007/s10955-017-1880-1 ISSN 0022-4715.
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Official URL: http://dx.doi.org/10.1007/s10955-017-1880-1
Abstract
Plaquette models are short range ferromagnetic spin models that play a key role in the dynamic facilitation approach to the liquid glass transition. In this paper we perform a rigorous study of the thermodynamic properties of two dimensional plaquette models, the square and triangular plaquette models. We prove that for any positive temperature both models have a unique infinite volume Gibbs measure with exponentially decaying correlations. We analyse the scaling of three a priori different static correlation lengths in the small temperature regime, the mixing, cavity and multispin correlation lengths. Finally, using the symmetries of the model we determine an exact self similarity property for the infinite volume Gibbs measure.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Journal or Publication Title: | Journal of Statistical Physics | ||||||||
Publisher: | Springer New York LLC | ||||||||
ISSN: | 0022-4715 | ||||||||
Official Date: | November 2017 | ||||||||
Dates: |
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Volume: | 169 | ||||||||
Number: | 3 | ||||||||
Page Range: | pp. 441-471 | ||||||||
DOI: | 10.1007/s10955-017-1880-1 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Open Access Version: |
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