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Pfaffian Correlation Functions of Planar Dimer Covers

Author(s): Aizenman, Michael; Lainz Valcazar, Manuel; Warzel, Simone

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Abstract: The Pfaffian structure of the boundary monomer correlation functions in the dimer-covering planar graph models is rederived through a combinatorial/topological argument. These functions are then extended into a larger family of order-disorder correlation functions which are shown to exhibit Pfaffian structure throughout the bulk. Key tools involve combinatorial switching symmetries which are identified through the loop-gas representation of the double dimer model, and topological implications of planarity.
Publication Date: Feb-2017
Electronic Publication Date: 3-Jan-2017
Citation: Aizenman, Michael, Lainz Valcazar, Manuel, Warzel, Simone. (2017). Pfaffian Correlation Functions of Planar Dimer Covers. JOURNAL OF STATISTICAL PHYSICS, 166 (1078 - 1091. doi:10.1007/s10955-016-1684-8
DOI: doi:10.1007/s10955-016-1684-8
ISSN: 0022-4715
EISSN: 1572-9613
Pages: 1078 - 1091
Type of Material: Journal Article
Version: Author's manuscript

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