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We examine connection matrices of Ising systems with long-rang interaction ond-dimensional hypercube lattices of linear dimensions L. We express theeigenvectors of these matrices as the Kronecker products of the eigenvectorsfor the one-dimensional Ising system. The eigenvalues of the connectionmatrices are polynomials of the d-th degree of the eigenvalues for theone-dimensional system. We show that including of the long-range interactiondoes not remove the degeneracy of the eigenvalues of the connection matrix. Weanalyze the eigenvalue spectral density in the limit L go to \infty. In thecase of the continuous spectrum, for d < 3 we obtain analytical formulas thatdescribe the influence of the long-range interaction on the spectral densityand the crucial changes of the spectrum.

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