Non-universal critical behaviour of random resistor networks with a singular distribution of conductances

A. Ben-Mizrahi, D. J. Bergman

Research output: Contribution to journalArticlepeer-review

Abstract

The critical properties of a random resistor network are investigated, using an infinitesimal Migdal-Kadanoff renormalisation group transformation, for cases where the non-zero conductors have a probability distribution h(g) which behaves as g- alpha, 0<or= alpha <1 for small g. A new fixed point is found, leading to a new type of critical behaviour of the bulk effective conductivity near the percolation threshold. The critical conductivity exponent t is found to depend on alpha , but differs from the value found by Kogut and Straley (1979) for this case. The crossover between the two types of critical behaviour, characterised by the different fixed points, is also discussed.

Original languageEnglish
Article number015
Pages (from-to)909-922
Number of pages14
JournalJournal of Physics C: Solid State Physics
Volume14
Issue number6
DOIs
StatePublished - 1981

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