SHARP THRESHOLDS FOR THE RANDOM-CLUSTER AND ISING MODELS

• 成果类型: Article
• 署名作者: Graham, Benjamin; Grimmett, Geoffrey
• 署名单位: University of British Columbia; Universite PSL; Ecole Normale Superieure (ENS); University of Cambridge
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP693
• 发表日期: 2011
• 页码: 240-265
• 关键词: critical probability; critical-behavior; PHASE-TRANSITION; percolation; magnetization; coexistence; uniqueness

摘要

A sharp-threshold theorem is proved for box-crossing probabilities on the square lattice. The models in question are the random-cluster model near the self-dual point p(sd)(q) = root q/(1 + root q), the Ising model with external field, and the colored random-cluster model. The principal technique is an extension of the influence theorem for monotonic probability measures applied to increasing events with no assumption of symmetry.