MIXING LENGTH SCALES OF LOW TEMPERATURE SPIN PLAQUETTES MODELS

P Chleboun , A Faggionato , F. Martinelli , C. Toninelli (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

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.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Mathématiques [math]

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