A Pfaffian formula for the Ising partition function of surface graphs
arXiv:2003.02967 · doi:10.1088/1742-5468/aba1e4
Abstract
We give a Pfaffian formula to compute the partition function of the Ising model on any graph 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 and the dimer model on its terminal graph . 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.