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Dimers on Graphs in Non-Orientable Surfaces

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Abstract

The main result of this article is a Pfaffian formula for the partition function of the dimer model on any graph Γ embedded in a closed, possibly non-orientable surface Σ. This formula is suitable for computational purposes, and it is obtained using purely geometrical methods. The key step in the proof consists of a correspondence between some orientations on Γ and the set of pin− structures on Σ. This generalizes (and simplifies) the results of a previous article (Cimasoni and Reshetikhin in Commun Math Phys 275:187–208, 2007).

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  1. Departement Mathematik, ETH Zurich, Rämistrasse 101, 8092, Zurich, Switzerland

    David Cimasoni

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  1. David Cimasoni
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Correspondence to David Cimasoni.

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Cimasoni, D. Dimers on Graphs in Non-Orientable Surfaces. Lett Math Phys 87, 149–179 (2009). https://doi.org/10.1007/s11005-009-0299-2

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  • DOI: https://doi.org/10.1007/s11005-009-0299-2

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