Email this article Connection-matrix eigenvalues in the Ising model: taking into account interaction with next-nearest neighbors
- Authors: Kryzhanovsky B.V.1, Litinskii L.B.1
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Affiliations:
- Federal State Institution «Scientific Research Institute for System Analysis of the Russian Academy of Sciences»
- Issue: Vol 489, No 3 (2019)
- Pages: 246-249
- Section: Theoretical physics
- URL: https://journals.eco-vector.com/0869-5652/article/view/18580
- DOI: https://doi.org/10.31857/S0869-56524893246-249
- ID: 18580
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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.
About the authors
B. V. Kryzhanovsky
Federal State Institution «Scientific Research Institute for System Analysis of the Russian Academy of Sciences»
Author for correspondence.
Email: kryzhanov@mail.ru
Corresponding Member of the Russian Academy of Sciences
Russian Federation, 36-1, Nakhimovsky prospect, Moscow, 117218L. B. Litinskii
Federal State Institution «Scientific Research Institute for System Analysis of the Russian Academy of Sciences»
Email: litin@mail.ru
Russian Federation, 36-1, Nakhimovsky prospect, Moscow, 117218
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