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Connection-Matrix Eigenvalues in the Ising Model: Taking into Account Interaction with Next-Nearest Neighbors
Doklady Physics ( IF 0.6 ) Pub Date : 2019-12-23 , DOI: 10.1134/s1028335819110065 B. V. Kryzhanovsky , L. B. Litinskii
中文翻译:
Ising模型中的连接矩阵特征值:考虑到与最近邻居的交互
更新日期:2019-12-23
Doklady Physics ( IF 0.6 ) Pub Date : 2019-12-23 , DOI: 10.1134/s1028335819110065 B. V. Kryzhanovsky , L. B. Litinskii
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:
Ising模型中的连接矩阵特征值:考虑到与最近邻居的交互