Conformal invariance of spin correlations in the planar Ising model

• 成果类型: Article
• 署名作者: Chelkak, Dmitry; Hongler, Clement; Izyurov, Konstantin
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2015.181.3.5
• 发表日期: 2015
• 页码: 1087-1138
• 关键词: probabilities; statistics; symmetry; surface

摘要

We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of conjectures coming from the physical and the mathematical literature. The proof relies on convergence results for discrete holomorphic spinor observables and probabilistic techniques.