Planar dimers and Harnack curves

@inproceedings{Kenyon2006PlanarDA,
  title={Planar dimers and Harnack curves},
  author={Richard A. Kenyon and Andrei Okounkov},
  year={2006}
}
In this paper we study the connection between dimers and Harnack curves discovered in [12]. To any periodic edge-weighted planar bipartite graph Γ one associates its spectral curve P (z, w) = 0. The real polynomial P defining the spectral curve arises as the characteristic polynomial of the Kasteleyn operator in the dimer model. It was shown in [12] that for real positive edge weights on Γ the curves thus obtained are real curves of a very special kind, namely they are Harnack curves. Harnack… CONTINUE READING

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