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APS » Journals » Phys. Rev. B » Volume 30 » Issue 7
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Phys. Rev. B 30, 4080–4082 (1984)

Superconductivity exponents in two- and three-dimensional percolation

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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

Received 9 February 1984; revised 22 May 1984; published in the issue dated 1 October 1984

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∼(p-pc)-s. We obtain very accurate values for the exponents which disagree with the Alexander-Orbach conjecture as well as other conjectures. Our results are s/ν=0.977±0.010 in two dimensions and s/ν=0.85±0.04 in three dimensions.

© 1984 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevB.30.4080
DOI:
10.1103/PhysRevB.30.4080
PACS:
 
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