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MIXING LENGTH SCALES OF LOW TEMPERATURE SPIN PLAQUETTES MODELS

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 mul-tispin correlation lengths. Finally, using the symmetries of the model we determine an exact self similarity property for the infinite volume Gibbs measure.
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https://hal.archives-ouvertes.fr/hal-01696428
Contributor : Cristina Toninelli <>
Submitted on : Tuesday, January 30, 2018 - 2:02:02 PM
Last modification on : Friday, April 10, 2020 - 5:26:48 PM
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  • HAL Id : hal-01696428, version 1

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P Chleboun, A Faggionato, F. Martinelli, C. Toninelli. MIXING LENGTH SCALES OF LOW TEMPERATURE SPIN PLAQUETTES MODELS. Journal of Statistical Physics, Springer Verlag, 2017. ⟨hal-01696428⟩

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