Influence of long-range interaction on degeneracy of eigenvalues of connection matrix of d-dimensional Ising system
| Autor: | Kryzhanovsky, B. V., Litinskii, L. B. |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8121/abbc4e |
| Popis: | We examine connection matrices of Ising systems with long-rang interaction on d-dimensional hypercube lattices of linear dimensions L. We express the eigenvectors of these matrices as the Kronecker products of the eigenvectors for the one-dimensional Ising system. The eigenvalues of the connection matrices are polynomials of the d-th degree of the eigenvalues for the one-dimensional system. We show that including of the long-range interaction does not remove the degeneracy of the eigenvalues of the connection matrix. We analyze the eigenvalue spectral density in the limit L go to \infty. In the case of the continuous spectrum, for d < 3 we obtain analytical formulas that describe the influence of the long-range interaction on the spectral density and the crucial changes of the spectrum. Comment: 10 pages, submitted in J. of Physics A |
| Databáze: | arXiv |
| Externí odkaz: |
|