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arxiv: 0804.4772 · v3 · pith:JWGGRSH2new · submitted 2008-04-30 · 🧮 math-ph · math.GT· math.MP

Dimers on graphs in non-orientable surfaces

classification 🧮 math-ph math.GTmath.MP
keywords formulanon-orientableclosedcomputationalconsistscorrespondencedimerdimers
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The main result of this paper is a Pfaffian formula for the partition function of the dimer model on a graph G embedded in a closed, possibly non-orientable surface S. 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 G and the set of pin^- structures on S. This generalizes (and simplifies) the results of a previous paper [2].

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