期刊
INVENTIONES MATHEMATICAE
卷 216, 期 3, 页码 661-743出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00222-018-00851-4
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资金
- NSF [PHY-1305472, DMS-1613296]
- NCCR SwissMAP
- IDEX grant from Paris-Saclay
- ERC CriBLaM
- Princeton University/University of Geneva partnership fund
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.
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