伊辛模型与正正交格拉斯曼
Ising model and the positive orthogonal Grassmannian
摘要：
本文用不等式完全描述了嵌入圆盘中的平面伊辛网络的边界相关矩阵集。具体地说，我们建立在M.~ Lis给出了这种相关矩阵与正交格拉斯曼的完全非负部分中的点之间的简单双射，该双射已于2013年在ABJM理论的散射振幅研究中引入。我们还表明，减少网络的伊辛模型的边缘参数可以唯一地从边界相关性恢复，解决了逆问题。在我们的对应下，Kramers-Wannier高/低温对偶变换为Grassmannian的循环对称，并利用这种循环对称，我们证明了所考虑的空间同胚于闭球.
英文摘要：
We completely describe by inequalities the set of boundary correlation matrices of planar Ising networks embedded in a disk. Specifically, we build on a recent result of M.~Lis to give a simple bijection between such correlation matrices and points in the totally nonnegative part of the orthogonal Grassmannian, which has been introduced in 2013 in the study of the scattering amplitudes of ABJM theory. We also show that the edge parameters of the Ising model for reduced networks can be uniquely recovered from boundary correlations, solving the inverse problem. Under our correspondence, the Kramers--Wannier high/low temperature duality transforms into the cyclic symmetry of the Grassmannian, and using this cyclic symmetry, we prove that the spaces under consideration are homeomorphic to closed balls.
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