Connection-Matrix Eigenvalues in the Ising Model: Taking into Account Interaction with Next-Nearest Neighbors

被引：9

作者：

Kryzhanovsky, B. V. ^{[1
]}

Litinskii, L. B. ^{[1
]}

机构：

[1] Russian Acad Sci, Sci Res Inst Syst Anal, Moscow 117218, Russia

来源：

DOKLADY PHYSICS | 2019年 / 64卷 / 11期

关键词：

Connection matrices - Eigenvalues and eigenvectors - Exact relations - Free boundary conditions - Hypercube - Nearest neighbors - One-dimensional Ising model;

D O I：

10.1134/S1028335819110065

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

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.

引用

页码：414 / 417

页数：4

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