ON MULTIPLE SLE FOR THE FK-ISING MODEL

• 成果类型: Article
• 署名作者: Izyurov, Konstantin
• 署名单位: University of Helsinki
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1547
• 发表日期: 2022
• 页码: 771-790
• 关键词: random-cluster model; erased random-walks; solution space; conformal-invariance; SCALING LIMITS; free-field; interfaces; SYSTEM; probabilities; combinatorics

摘要

We prove the convergence of multiple interfaces in the critical planar q = 2 random cluster model and provide an explicit description of the scaling limit. Remarkably, the expression for the partition function of the resulting multiple SLE16/3 coincides with the bulk spin correlation in the critical Ising model in the half-plane, after formally replacing a position of each spin and its complex conjugate with a pair of points on the real line. As a corollary we recover Belavin-Polyakov-Zamolodchikov equations for the spin correlations.