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Resistance distribution in the hopping percolation model

Yakov M. Strelniker·Shlomo Havlin·Richard Berkovits·Aviad Frydman
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Abstract

We study the distribution function, P(rho), of the effective resistance, rho, in two and three-dimensional random resistor network of linear size L in the hopping percolation model. In this model each bond has a conductivity taken from an exponential form σ~ exp(-kappa r), where kappa is a measure of disorder, and r is a random number, 0< r < 1. We find that in both the usual strong disorder regime L/kappa^{nu} > 1 (not sensitive to removal of any single bond) and the extreme disorder regime L/kappa^{nu} < 1 (very sensitive to such a removal) the distribution depends only on L/kappa^{nu} and can be well approximated by a log-normal function with dispersion b kappa^nu/L, where b is a coefficient which depends on the type of the lattice

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Yakov M. Strelniker, Shlomo Havlin, Richard Berkovits, Aviad Frydman. 2005-06-07. Resistance distribution in the hopping percolation model. https://doi.org/10.1103/physreve.72.016121

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