Partition function of periodic isoradial dimer models

Details Partition function of periodic isoradial dimer models Partition function of periodic isoradial dimer models

2006-05-22

arxiv.org/abs/math/0605583v1

Probab. Theory Related Fields 138 (2007), no. 3-4, 451--462.

Mathematics

Probability

12 pages, 2 figures

Scientific paper

Isoradial dimer models were introduced in \cite{Kenyon3} - 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 \cite{Kenyon3}, 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 \cite{KOS}.

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