Dimers on surface graphs and spin structures. II

Details Dimers on surface graphs and spin structures. II Dimers on surface graphs and spin structures. II

2007-04-02

arxiv.org/abs/0704.0273v1

Physics

Mathematical Physics

23 pages, 3 figures

Scientific paper

10.1007/s00220-008-0488-3

In a previous paper, we showed how certain orientations of the edges of a graph G embedded in a closed oriented surface S can be understood as discrete spin structures on S. We then used this correspondence to give a geometric proof of the Pfaffian formula for the partition function of the dimer model on G. In the present article, we generalize these results to the case of compact oriented surfaces with boundary. We also show how the operations of cutting and gluing act on discrete spin structures and how they change the partition function. These operations allow to reformulate the dimer model as a quantum field theory on surface graphs.

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