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Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices

ContributorsCimasoni, David
Number of pages39
Publication date2009
Abstract

Let S be a flat surface of genus g with cone type singularities. Given a bipartite graph G isoradially embedded in S, we define discrete analogs of the 2^{2g} Dirac operators on S. 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 (S,G) for these discrete Dirac operators to be Kasteleyn matrices of the graph G. As a consequence, if these conditions are met, the partition function of the dimer model on G can be explicitly written as an alternating sum of the determinants of these 2^{2g} discrete Dirac operators.

Classification
  • arxiv : math-ph
NoteSoumis dans : Journal of the European Mathematical Society
Affiliation Not a UNIGE publication
Citation (ISO format)
CIMASONI, David. Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices. 2009, p. 39.
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