Dimers on Surface Graphs and Spin Structures. I

2006/08/31 by David Cimasoni, Nicolai Reshetikhin · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Combinatorics #Geometric and Algebraic Topology #Geometry #Graph #Mathematics #Partition (number theory) #Physics #Pure mathematics #Spin (aerodynamics) #Surface (topology) #Thermodynamics #Topological and Geometric Data Analysis #math-ph #math.GT #math.MP #msc:57R15 #msc:82B20

paper · pdf · doi:10.1007/s00220-007-0302-7

published as Comm. Math. Phys. 275 (2007), 187-208 · 21 pages, 8 figures, minor modifications

arxiv created 2006/09/27 · openalex publication_date 2007/07/24 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Partition functions for dimers on closed oriented surfaces are known to be alternating sums of Pfaffians of Kasteleyn matrices. In this paper, we obtain the formula for the coefficients in terms of discrete spin structures.

Citations

• Dimers and amoebae

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