A new correlation inequality for Ising models with external fields

• 成果类型: Article
• 署名作者: Ding, Jian; Song, Jian; Sun, Rongfeng
• 署名单位: Peking University; Shandong University; Shandong University; National University of Singapore
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01132-1
• 发表日期: 2023
• 页码: 477-492
• 关键词: phase-transition; glauber dynamics; spin systems; cutoff

摘要

We study ferromagnetic Ising models on finite graphs with an inhomogeneous external field, where a subset of vertices is designated as the boundary. We show that the influence of boundary conditions on any given spin is maximised when the external field is identically 0. One corollary is that spin-spin correlations are maximised when the external field vanishes and the boundary condition is free, which proves a conjecture of Shlosman. In particular, the random field Ising model on Z(d), d >= 3, exhibits exponential decay of correlations in the entire high temperature regime of the pure Ising model. Another corollary is that the pure Ising model in d >= 3 satisfies the conjectured strong spatial mixing property in the entire high temperature regime.