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Eigenvalues of a statistical mechanics matrix

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Abstract

We consider the problem of finding the spectrum of an n × n matrix which arises in the study of a certain model of long-range interactions in a one-dimensional statistical mechanics system. Our analysis exhibits a curious resemblance of the suitably normalized distribution of eigenvalues to the Marčenko–Pastur law in the limit n → ∞.

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Authors and Affiliations

  1. Instituto de Física y Matemáticas, Universidad Tecnológica de la Mixteca, Huajuapan de León, 69000, Mexico

    Wolfgang P. Angerer

  2. Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana—Cuajimalpa, México, D.F., 01120, Mexico

    Adolfo Zamora

Authors
  1. Wolfgang P. Angerer
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  2. Adolfo Zamora
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Correspondence to Wolfgang P. Angerer.

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Angerer, W.P., Zamora, A. Eigenvalues of a statistical mechanics matrix. J Math Chem 50, 1411–1419 (2012). https://doi.org/10.1007/s10910-012-9980-2

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  • DOI: https://doi.org/10.1007/s10910-012-9980-2

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