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Interpretation of high-dimensional numerical results for the Anderson transition

  • Special issue in honor of A.F. Andreev’s 75th birthday Issue Editor: I.A. Fomin
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Abstract

The existence of the upper critical dimension d c2 = 4 for the Anderson transition is a rigorous consequence of the Bogoliubov theorem on renormalizability of φ4 theory. For d ≥ 4 dimensions, one-parameter scaling does not hold and all existent numerical data should be reinterpreted. These data are exhausted by the results for d = 4, 5 from scaling in quasi-one-dimensional systems and the results for d = 4, 5, 6 from level statistics. All these data are compatible with the theoretical scaling dependences obtained from Vollhardt and Wolfle’s self-consistent theory of localization. The widespread viewpoint that d c2 = ∞ is critically discussed.

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Authors and Affiliations

  1. Kapitza Institute for Physical Problems, Russian Academy of Sciences, Moscow, 119334, Russia

    I. M. Suslov

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  1. I. M. Suslov
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Correspondence to I. M. Suslov.

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Published in Russian in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2014, Vol. 146, No. 6, pp. 1272–1281.

Contribution for the JETP special issue in honor of A.F. Andreev’s 75th birthday

The article was translated by the author.

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Suslov, I.M. Interpretation of high-dimensional numerical results for the Anderson transition. J. Exp. Theor. Phys. 119, 1115–1122 (2014). https://doi.org/10.1134/S1063776114120188

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  • DOI: https://doi.org/10.1134/S1063776114120188

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