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arXiv · 2008.04227

Influence of long-range interaction on degeneracy of eigenvalues of connection matrix of d-dimensional Ising system

B. V. Kryzhanovsky·L. B. Litinskii
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Abstract

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.

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B. V. Kryzhanovsky, L. B. Litinskii. 2020-08-10. Influence of long-range interaction on degeneracy of eigenvalues of connection matrix of d-dimensional Ising system. https://doi.org/10.1088/1751-8121%2Fabbc4e

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