A finite-volume version of Aizenman-Higuchi theorem for the 2d Ising model

• 成果类型: Article
• 署名作者: Coquille, Loren; Velenik, Yvan
• 署名单位: University of Geneva
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-011-0339-6
• 发表日期: 2012
• 页码: 25-44
• 关键词: phase-separation line; ornstein-zernike theory; surface-tension; coexistence; connectivities; percolation; Invariance; SYSTEM; STATES

摘要

In the late 1970s, in two celebrated papers, Aizenman and Higuchi independently established that all infinite-volume Gibbs measures of the two-dimensional ferromagnetic nearest-neighbor Ising model at inverse temperature are of the form , where and are the two pure phases and . We present here a new approach to this result, with a number of advantages: (a) We obtain an optimal finite-volume, quantitative analogue (implying the classical claim); (b) the scheme of our proof seems more natural and provides a better picture of the underlying phenomenon; (c) this new approach might be applicable to systems for which the classical method fails.