伊辛模型中的费米子可观测量与逆Kac-Ward算符
The fermionic observable in the Ising model and the inverse Kac-Ward operator
摘要：
我们证明了等径图上的临界Kac-Ward算子在一定意义上起着s-全纯算子的作用，并将自旋伊辛模型的费米子可观测量确定为该算子的逆算子.这个结果部分是一个更普遍的观察结果，即任何平面图的逆Kac-Ward算子是由我们称为费米子生成函数给出的。此外，使用的Kac-Ward转移矩阵的谱半径和运营商的范数的界限，我们提供了一个一般的图片的非回溯行走表示的临界和超临界逆Kac-Ward运营商等径图。
英文摘要：
We show that the critical Kac-Ward operator on isoradial graphs acts in a certain sense as the operator of s-holomorphicity, and we identify the fermionic observable for the spin Ising model as the inverse of this operator. This result is partially a consequence of a more general observation that the inverse Kac-Ward operator for any planar graph is given by what we call a fermionic generating function. Furthermore, using bounds for the spectral radius and operator norm of the Kac-Ward transition matrix, we provide a general picture of the non-backtracking walk representation of the critical and supercritical inverse Kac-Ward operators on isoradial graphs.
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