Abstract

We analyze a finite one-dimensional Ising system with periodic boundary conditions taking into account an arbitrary long-range interaction. We examine a discrete spectrum of eigenvalues of the spin connection matrix and a spectrum density of a continuous distribution obtained in the limit \(L \to \infty \) (L is the linear size of the system). We apply our results to particular cases of long-range interactions decreasing with distance.

中文翻译：

---

一维伊辛模型中远程交互对连接矩阵特征值的影响

摘要

我们分析了具有周期性边界条件的有限一维Ising系统，其中考虑了任意远程交互作用。我们检查了自旋连接矩阵的特征值的离散频谱以及在极限\（L \ to \ infty \）中获得的连续分布的频谱密度（L是系统的线性大小）。我们将研究结果应用于远距离相互作用随距离减少的特殊情况。