Abstract

The connection matrix of the Ising model on a \(d\)-dimensional hypercube is investigated. In addition to the interactions between the nearest neighbors, the interactions between the next-nearest neighbors are taken into account. For such a matrix, the exact relations for the eigenvalues and eigenvectors, which are reasonably simply expressed through the corresponding characteristics of the one-dimensional Ising model, are obtained. Both periodic and free boundary conditions are considered.

中文翻译：

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Ising模型中的连接矩阵特征值：考虑到与最近邻居的交互

摘要

研究了\（d \）维超立方体上Ising模型的连接矩阵。除了最近邻居之间的交互之外，还要考虑下一个最近邻居之间的交互。对于这样的矩阵，获得了特征值和特征向量的精确关系，这些关系通过一维伊辛模型的相应特征合理地简单表示。同时考虑了周期性和自由边界条件。