The connective constant of the honeycomb lattice equals √2+√2

• 成果类型: Article
• 署名作者: Duminil-Copin, Hugo; Smirnov, Stanislav
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.175.3.14
• 发表日期: 2012
• 页码: 1653-1665
• 关键词: models

摘要

We provide the first mathematical proof that the connective constant of the hexagonal lattice is equal to root 2 + root 2 This value has been derived nonrigorously by B. Nienhuis in 1982, using Coulomb gas approach from theoretical physics. Our proof uses a parafermionic observable for the self-avoiding walk, which satisfies a half of the discrete Cauchy-Riemann relations. Establishing the other half of the relations (which conjecturally holds in the scaling limit) would also imply convergence of the self-avoiding walk to SLE(8/3).