Resistance distribution in the hopping percolation model

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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/kappanu > 1 (not sensitive to removal of any single bond) and the extreme disorder regime L/kappanu < 1 (very sensitive to such a removal) the distribution depends only on L/kappanu and can be well approximated by a log-normal function with dispersion b kappaⁿu/L, where b is a coefficient which depends on the type of the lattice