Geometric effects in continuous-media percolation

Ping Sheng, Robert Kohn

Research output: Contribution to journalArticle

Abstract

We study the simple system of a two-dimensional square lattice composed of good-conductor and poor-conductor squares, with the use of a clustered mean-field approximation. Instead of the well-known threshold behavior predicted by the two-component site percolation model or the effective-medium theory, we find two conductivity percolation thresholds at which the real and imaginary parts of the effective dielectric constant exhibit distinct critical behaviors. The cause of this double-threshold characteristic is shown to be the existence of a third conductivity scale arising from the corner-corner interactions between second-nearest-neighbor squares. Analogies with site percolation models are also detailed. It is demonstrated that as |12|, where 1(2) is the complex dielectric constant of the good (poor) conductor, the continuum system can be made equivalent to two versions of the square-lattice site percolation model, depending on whether |1| or |2|0. The paper concludes with a discussion of possible implications for three-dimensional continuous-media percolating systems.

Original languageEnglish (US)
Pages (from-to)1331-1335
Number of pages5
JournalPhysical Review B
Volume26
Issue number3
DOIs
StatePublished - 1982

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conductors
Permittivity
thresholds
permittivity
conductivity
continuums
causes
approximation
interactions

ASJC Scopus subject areas

  • Condensed Matter Physics

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Geometric effects in continuous-media percolation. / Sheng, Ping; Kohn, Robert.

In: Physical Review B, Vol. 26, No. 3, 1982, p. 1331-1335.

Research output: Contribution to journalArticle

Sheng, Ping ; Kohn, Robert. / Geometric effects in continuous-media percolation. In: Physical Review B. 1982 ; Vol. 26, No. 3. pp. 1331-1335.
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