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Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices

David Cimasoni (2012)

Journal of the European Mathematical Society

Let be a flat surface of genus g with cone type singularities. Given a bipartite graph Γ isoradially embedded in , we define discrete analogs of the 2 2 g Dirac operators on . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair Γ for these discrete Dirac operators to be Kasteleyn matrices of the graph Γ . As a consequence, if these conditions are met, the partition function of the dimer...

Dreieckszerlegungen

Werner Raffke (1991)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Currently displaying 1 – 3 of 3

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