On the Gibbs states of the noncritical Potts model on Z2

• 成果类型: Article
• 署名作者: Coquille, Loren; Duminil-Copin, Hugo; Ioffe, Dmitry; Velenik, Yvan
• 署名单位: University of Geneva; Technion Israel Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0486-z
• 发表日期: 2014
• 页码: 477-512
• 关键词: 2-dimensional ising-model; phase-separation line; pirogov-sinai theory; boundary-conditions; exponential decay; coexistence; connectivities; percolation; Invariance

摘要

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 beta > beta(c)(q) = log (1 + root q).