Transfer matrix calculation of conductivity in three-dimensional random resistor networks at percolation threshold
- 1 January 1983
- journal article
- Published by EDP Sciences in Journal de Physique Lettres
- Vol. 44 (17) , 701-706
- https://doi.org/10.1051/jphyslet:019830044017070100
Abstract
For very long bars of size n x n x L, with L >> n, and n up to 18, we calculate the conductivity of a random network of resistors and insulators. At the percolation threshold in a simple cubic lattice our Monte Carlo data give a conductivity decreasing with bar diameter n as n-2.1 for site and bond percolation. Taking into account corrections to scaling with a correction exponent ω near unity, our best estimate for the conductivity exponent t is t/v = 2.2 ± 0.1 in both the bond and the site cases. These results strongly support the Alexander-Orbach [8] conjecture t/v ≃ 2.26 for the conductivity exponent in three dimensionsKeywords
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