Critical phenomena in resistor networks

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172 Scopus citations


The conduction threshold which occurs in resistor networks when a certain fraction has zero conductivity can be treated as a sort of critical point. This critical point is also relevant to mixtures of resistors with finite conductivities a and b, in the limit a<<b. A homogeneous function representation is proposed for the conductivity in the vicinity of the conduction threshold and a parametric representation is also given. This representation makes predictions for the concentration (p) and composition (a/b) dependence of such networks which are consistent with the behaviour of the Bethe lattice model recently proposed by Stinchcombe (1973, 1974). The frequency dependence of the impedance is also discussed and a correlation length which diverges at the critical point is described.

Original languageEnglish
Article number017
Pages (from-to)783-795
Number of pages13
JournalJournal of Physics C: Solid State Physics
Issue number5
StatePublished - 1976

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Engineering (all)
  • Physics and Astronomy (all)


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