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arXiv · 2003.02967

A Pfaffian formula for the Ising partition function of surface graphs

Anh Minh Pham
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Abstract

We give a Pfaffian formula to compute the partition function of the Ising model on any graph $G$ embedded in a closed, possibly non-orientable surface. This formula, which is suitable for computational purposes, is based on the relation between the Ising model on $G$ and the dimer model on its terminal graph $G^T$. By combining the ideas of Loebl-Masbaum \cite{Loeb11}, Tesler \cite{Tes2000}, Cimasoni \cite{Cim09, Cim10} and Chelkak-Cimasoni-Kassel \cite{Chel15}, we give an elementary proof for the formula.

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Anh Minh Pham. 2020-03-05. A Pfaffian formula for the Ising partition function of surface graphs. https://doi.org/10.1088/1742-5468%2Faba1e4

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