Emergent planarity in two-dimensional Ising models with finite-range Interactions

• 成果类型: Article
• 署名作者: Aizenman, Michael; Duminil-Copin, Hugo; Tassion, Vincent; Warzel, Simone
• 署名单位: Princeton University; Universite Paris Saclay; University of Geneva; Swiss Federal Institutes of Technology Domain; ETH Zurich; Technical University of Munich
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-00851-4
• 发表日期: 2019
• 页码: 661-743
• 关键词: correlation inequalities

摘要

The known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological considerations within the model's random current representation. This perspective is then employed in the proof that the Pfaffian structure of boundary correlations emerges asymptotically at criticality in Ising models on Z2 with finite-range interactions. The analysis is enabled by new results on the stochastic geometry of the corresponding random currents. The proven statement establishes an aspect of universality, seen here in the emergence of fermionic structures in two dimensions beyond the solvable cases.