Abstract
Isoradial dimer models were introduced in Kenyon (Invent Math 150(2):409–439, 2002)—they consist of dimer models whose underlying graph satisfies a simple geometric condition, and whose weight function is chosen accordingly. In this paper, we prove a conjecture of (Kenyon in Invent Math 150(2):409–439, 2002), namely that for periodic isoradial dimer models, the growth rate of the toroidal partition function has a simple explicit formula involving the local geometry of the graph only. This is a surprising feature of periodic isoradial dimer models, which does not hold in the general periodic dimer case (Kenyon et al. in Ann Math, 2006).
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de Tilière, B. Partition function of periodic isoradial dimer models. Probab. Theory Relat. Fields 138, 451–462 (2007). https://doi.org/10.1007/s00440-006-0041-2
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DOI: https://doi.org/10.1007/s00440-006-0041-2
Mathematics Subject Classification (2000)
- 82B20