论文标题
表面图的Ising分区函数的PFAFFIAN公式
A Pfaffian formula for the Ising partition function of surface graphs
论文作者
论文摘要
我们给出一个PFAFFIAN公式，以在任何嵌入在封闭的，可能是不可方向的表面中的图形$ g $上计算Ising模型的分区函数。此公式适合计算目的，基于$ g $上的Ising模型与终端图$ g^t $上的二聚体模型之间的关系。通过结合Loebl-Masbaum \ Cite {Loeb11}的想法，Tesler \ Cite {Tes2000}，Cimasoni \ cite {CIM09，CIM10}和Chelkak-Cimasoni-Kassel \ cite {chel15}，我们提供元素的证明。
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.
