Scientific article
Open access

Dimers on surface graphs and spin structures. II

Published inCommunications in Mathematical Physics, vol. 281, no. 2, p. 445-468
Publication date2008

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.

  • arxiv : math-ph
Note3 figures
Affiliation Not a UNIGE publication
Citation (ISO format)
CIMASONI, David, RESHETIKHIN, Nicolai. Dimers on surface graphs and spin structures. II. In: Communications in Mathematical Physics, 2008, vol. 281, n° 2, p. 445–468. doi: 10.1007/s00220-008-0488-3
Updates (1)
ISSN of the journal1432-0916

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