On the Gibbs states of the noncritical Potts model on

We prove that all Gibbs states of the -state nearest neighbor Potts model on below the critical temperature are convex combinations of the pure phases; in particular, they are all translation invariant. To achieve this goal, we consider such models in large finite boxes with arbitrary boundary condi...

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Bibliographic Details
Published in:Probability theory and related fields 2014-02, Vol.158 (1-2), p.477-512
Main Authors: Coquille, Loren, Duminil-Copin, Hugo, Ioffe, Dmitry, Velenik, Yvan
Format: Article
Language:English
Subjects:
Boundary conditions
Critical temperature
Economics
Finance
Fluctuation
Insurance
Invariants
Inverse
Management
Mathematical analysis
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Phases
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Statistics for Business
Texts
Theoretical
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Summary:We prove that all Gibbs states of the -state nearest neighbor Potts model on below the critical temperature are convex combinations of the 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 .
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-013-0486-z