Resistance distribution in the hopping percolation model
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 \sigma ~ 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
Cite
@article{arxiv.cond-mat/0506179,
title = {Resistance distribution in the hopping percolation model},
author = {Yakov M. Strelniker and Shlomo Havlin and Richard Berkovits and Aviad Frydman},
journal= {arXiv preprint arXiv:cond-mat/0506179},
year = {2009}
}
Comments
Phys Rev E (in press)