Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Influence of long-range interaction on degeneracy of eigenvalues of
  connection matrix of d-dimensional Ising system   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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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc