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On the Gibbs states of the noncritical Potts model on Z^2

Publié dansProbability theory and related fields, vol. 158, p. 477-512
Date de publication2014
Résumé

We prove that all Gibbs states of the q-state nearest neighbor Potts model on Z^2 below the critical temperature are convex combinations of the q pure phases; in particular, they are all translation invariant. To achieve this goal, we consider such models in large finite boxes with arbitrary boundary condition, and prove that the center of the box lies deeply inside a pure phase with high probability. Our estimate of the finite-volume error term is of essentially optimal order, which stems from the Brownian scaling of fluctuating interfaces. The results hold at any supercritical value of the inverse temperature.

Classification
  • arxiv : math.PR
Citation (format ISO)
COQUILLE, Loren et al. On the Gibbs states of the noncritical Potts model on Z^2. In: Probability theory and related fields, 2014, vol. 158, p. 477–512. doi: 10.1007/s00440-013-0486-z
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Identifiants
ISSN du journal0178-8051
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Informations techniques

Création22/05/2012 13:20:00
Première validation22/05/2012 13:20:00
Heure de mise à jour14/03/2023 17:36:51
Changement de statut14/03/2023 17:36:51
Dernière indexation15/01/2024 23:56:32
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