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Superconductivity exponents in two- and three-dimensional percolation

H. J. Herrmann, B. Derrida, and J. Vannimenus
Phys. Rev. B 30, 4080(R) – Published 1 October 1984
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Abstract

The first transfer-matrix calculation of the superconductivity exponent s of a random mixture of normal and superconducting elements is presented: The exponent s is defined through the divergence of the conductivity Σ as the critical fraction pc of superconducting elements is approached: Σ(ppc)s. We obtain very accurate values for the exponents which disagree with the Alexander-Orbach conjecture as well as other conjectures. Our results are sν=0.977±0.010 in two dimensions and sν=0.85±0.04 in three dimensions.

  • Received 9 February 1984

DOI:https://doi.org/10.1103/PhysRevB.30.4080

©1984 American Physical Society

Authors & Affiliations

H. J. Herrmann and B. Derrida

  • Service de Physique Théorique, Centre d'Etudes Nucléaires de Saclay, F-91191 Gif-sur-Y vette Cedex, France

J. Vannimenus

  • Laboratoire de Physique des Solides, Ecole Normale Supérieure, 24 rue Lhomond, F-75231 Paris Cedex 05, France

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Issue

Vol. 30, Iss. 7 — 1 October 1984

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