标题： 立方映射上的伊辛模型：任意亏格 显示英文标题

标题： The Ising model on cubic maps: arbitrary genus

摘要： 我们设计了一个递归算法来计算Ising模型的配分函数，该函数针对固定大小和亏格的立方映射进行了求和。该算法以多项式时间运行，比基于Tutte类似或拓扑递归的方法快得多。我们从KP方程组的第一个方程出发，推导出一个偏微分方程，并以此构建了这个算法。这一级数确实通过变量替换与Ising配分函数相关联。我们还得到了该配分函数系数的一些不等式，这些不等式应该有助于对亏格随大小线性增长的立方Ising映射进行概率研究。 显示英文摘要

摘要： We design a recursive algorithm to compute the partition function of the Ising model, summed over cubic maps with fixed size and genus. The algorithm runs in polynomial time, which is much faster than methods based on a Tutte-like, or topological, recursion. We construct this algorithm out of a partial differential equation that we derive from the first equation of the KP hierarchy satisfied by the generating function of bipartite maps. This series is indeed related to the Ising partition function by a change of variables. We also obtain inequalities on the coefficients of this partition function, which should be useful for a probabilistic study of cubic Ising maps whose genus grows linearly with their size.