On the double random current nesting field

• 成果类型: Article
• 署名作者: Duminil-Copin, Hugo; Lis, Marcin
• 署名单位: University of Geneva; University of Vienna
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-019-00899-0
• 发表日期: 2019
• 页码: 937-955
• 关键词: phase-transition; MODEL; dimers

摘要

We relate the planar random current representation introduced by Griffiths, Hurst and Sherman to the dimer model. More precisely, we provide a measure-preserving map between double random currents (obtained as the sum of two independent random currents) on a planar graph and dimers on an associated bipartite graph. We also define a nesting field for the double random current, which, under this map, corresponds to the height function of the dimer model. As applications, we provide an alternative derivation of some of the bozonization rules obtained recently by Dubedat, and show that the spontaneous magnetization of the Ising model on a planar biperiodic graph vanishes at criticality.