伊辛网络的二元性
Dualities for Ising networks
摘要：
本文研究了平面伊辛网络与正正交格拉斯曼网络中胞的等价性。我们提出了一种基于合并的微观结构，它建立了任何平面伊辛网络的对应关系。等价性允许我们引入两种计算Ising网络的递归方法。第一种基于对偶运动，它生成属于格拉斯曼运动中同一细胞的网络。这导致分形晶格的递归公式成为确切的RG方程的有效耦合。对于第二个，我们使用合并，其中每次迭代将种子格的大小加倍。这导致了一种有效的方法来计算相关器，其中复杂性相对于自旋位点的数量以几何方式缩放。
英文摘要：
In this note, we study the equivalence between planar Ising networks and cells in the positive orthogonal Grassmannian. We present a microscopic construction based on amalgamation, which establishes the correspondence for any planar Ising network. The equivalence allows us to introduce two recursive methods for computing correlators of Ising networks. The first based on duality moves, which generate networks belonging to the same cell in the Grassmannian. This leads to fractal lattices where the recursion formulas become the exact RG equations of the effective couplings. For the second, we use amalgamation where each iteration doubles the size of the seed lattice. This leads to an efficient way of computing the correlator where the complexity scales logarithmically with respect to the number of spin sites.
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