Monopole-Dimer模型的平方
Squareness for the Monopole-Dimer model
摘要：
最近引入的二聚体-二聚体模型是二聚体模型的一个精确可解的广义符号。我们证明了在不动点自由对合下，图不变量上的二聚体-二聚体模型的分拆函数是一个完满平方。我们给出了一个组合解释的平方根的分拆函数，这样的图在一个新的一类图的两种类型的边缘，我们称之为双子叶植物的双聚体模型。后者的分拆函数可以写成行列式，这次是一个复杂的邻接矩阵。该公式推广了T. T.平面双子格子图的虚定向的吴氏赋值。作为应用，我们计算了一类具有正权的非平面双子族的分拆函数。
英文摘要：
The monopole-dimer model introduced recently is an exactly-solvable signed generalisation of the dimer model. We show that the partition function of the monopole-dimer model on a graph invariant under a fixed-point free involution is a perfect square. We give a combinatorial interpretation of the square-root of the partition function for such graphs in terms of a monopole-dimer model on a new kind of graph with two types of edges which we call a dicot. The partition function of the latter can be written as a determinant, this time of a complex adjacency matrix. This formulation generalises T. T. Wu's assignment of imaginary orientation for the grid graph to planar dicots. As an application, we compute the partition function for a family of non-planar dicots with positive weights.
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