Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices

DOI10.4171/JEMS/331zbMath1243.82017arXiv0909.5339OpenAlexW2594331066MaRDI QIDQ437817

David Cimasoni

Publication date: 20 July 2012

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.5339

zbMATH Keywords

Dirac operatorperfect matchingdimer modeldiscrete complex analysisisoradial graphKasteleyn matrices

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Relations of low-dimensional topology with graph theory (57M15) Discrete geometry (52C99)

Related Items (5)

Discrete Riemann surfaces based on quadrilateral cellular decompositions ⋮ Universality of spin correlations in the Ising model on isoradial graphs ⋮ Discrete Dirac operators, critical embeddings and Ihara-Selberg functions ⋮ The critical Ising model via Kac-Ward matrices ⋮ Kac-Ward operators, Kasteleyn operators, and \(s\)-holomorphicity on arbitrary surface graphs

Cites Work

• Unnamed Item
• Unnamed Item
• Discrete complex analysis on isoradial graphs
• Dimers on graphs in non-orientable surfaces
• Theta functions, modular invariance, and strings
• An exploration of the permanent-determinant method
• On the theory of Pfaffian orientations. I: Perfect matchings and permanents
• The Laplacian and Dirac operators on critical planar graphs
• Dimers on surface graphs and spin structures. I
• The statistics of dimers on a lattice
• Spin Structures and Quadratic forms on Surfaces
• Riemann surfaces and spin structures
• Potential theory on a rhombic lattice
• Dimers and the critical Ising model on lattices of genus \(>1\)

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