### 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 language | English (US) |
---|---|

Pages (from-to) | 1331-1335 |

Number of pages | 5 |

Journal | Physical Review B |

Volume | 26 |

Issue number | 3 |

DOIs | |

State | Published - 1982 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B*,

*26*(3), 1331-1335. https://doi.org/10.1103/PhysRevB.26.1331

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

Research output: Contribution to journal › Article

*Physical Review B*, vol. 26, no. 3, pp. 1331-1335. https://doi.org/10.1103/PhysRevB.26.1331

}

TY - JOUR

T1 - Geometric effects in continuous-media percolation

AU - Sheng, Ping

AU - Kohn, Robert

PY - 1982

Y1 - 1982

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevB.26.1331

DO - 10.1103/PhysRevB.26.1331

M3 - Article

VL - 26

SP - 1331

EP - 1335

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 3

ER -