Resistance distribution in the hopping percolation model

We study the distribution function P(ρ) of the effective resistance ρ in two- and three-dimensional random resistor networks of linear size L in the hopping percolation model. In this model each bond has a conductivity taken from an exponential form σ exp(-κr), where κ 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 κν>1 (not sensitive to removal of any single bond) and the extreme-disorder regime L κν<1 (very sensitive to such a removal) the distribution depends only on L κν and can be well approximated by a log-normal function with dispersion bκν L, where b is a coefficient which depends on the type of lattice, and ν is the correlation critical exponent.