Critical exponents for the conductivity of random resistor lattices

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376 Scopus citations

Abstract

This paper presents three results concerning the critical exponents which characterize the conduction threshold of a resistor lattice. (a) There are no rigorous inequalities similar to those for the phase-transition critical exponents. (b) There is a dual transformation in two dimensions which relates the critical exponents: in particular s=t, u=12 for the two-dimensional bond problem. (c) The exponents for the two- and three-dimensional bond and site problems are estimated by numerically solving for the voltage distributions of large finite disordered lattices. The results are in agreement with the "scaling" exponent relationship.

Original languageEnglish
Pages (from-to)5733-5737
Number of pages5
JournalPhysical Review B
Volume15
Issue number12
DOIs
StatePublished - 1977

ASJC Scopus subject areas

  • Condensed Matter Physics

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