Random walks on bond percolation clusters: ac hopping conductivity below the threshold

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Abstract

The frequency dependence of the ac hopping conductivity in two and three dimensional lattices with random interruptions is calculated by Monte Carlo simulation of random walks on bond percolation clusters. At low frequencies the real and imaginary parts of the ac conductivity vanish linearly and quadratically with the frequency, respectively. The critical behaviour of the imaginary part of the ac conductivity below the percolation threshold is shown to depend on the long time limit of the mean square displacement of random walks R2, while the real part depends on the time constant of the system as well. R2 is found to diverge with an exponent u=2ν-β according to the conjecture of Stauffer.

Original languageEnglish
Pages (from-to)153-157
Number of pages5
JournalZeitschrift für Physik B Condensed Matter
Volume45
Issue number2
DOIs
Publication statusPublished - Jun 1981

ASJC Scopus subject areas

  • Condensed Matter Physics

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