Transfer matrix calculation of conductivity in three-dimensional random resistor networks at percolation threshold

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 dimensions.