A Pfaffian formula for the Ising partition function of surface graphs
Mathematical Physics
2020-08-26 v1 math.MP
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.
Keywords
Cite
@article{arxiv.2003.02967,
title = {A Pfaffian formula for the Ising partition function of surface graphs},
author = {Anh Minh Pham},
journal= {arXiv preprint arXiv:2003.02967},
year = {2020}
}