TRANSLATION-INVARIANT GIBBS STATES OF THE ISING MODEL: GENERAL SETTING

• 成果类型: Article
• 署名作者: Raoufi, Aran
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1374
• 发表日期: 2020
• 页码: 760-777
• 关键词: phase-transitions; magnetization; coexistence; percolation

摘要

We prove that at any inverse temperature beta and on any transitive amenable graph, the automorphism-invariant Gibbs states of the ferromagnetic Ising model are convex combinations of the plus and minus states. The theorem is equivalent with the differentiability of the free energy with respect to the temperature at any temperature. This is obtained for a general class of interactions, that is automorphism-invariant and irreducible coupling constants. The proof uses the random current representation of the Ising model. The result is novel when the graph is not Z(d), or when the graph is Z(d) but endowed with infinite-range interactions, or even Z(2) with finite-range interactions. Among the other corollaries of this result, we can list continuity of the magnetization at any noncritical temperature and the uniqueness of FK-Ising infinite-volume measures at any temperature.