Current distributions in a two-dimensional random-resistor network

Abstract

The current and logarithm-of-the-current distributionsn(∣i∣) andn(∣ln ∣i∣∣) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (−9⩽k⩽8) of n(∣ln ∣i∣∣) i.e., 〈∣ln ∣i&∣∣^k〉, is found to scale with the linear sizeL as (InL)^β(k). The exponents β(k) are not inconsistent with the recent theoretical prediction β(k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y)≈−γγ, yielding information on the threshold below which the multifractality of$\hat n$(∣i∣) breaks down. Our numerical results for the moments of the currents are consistent with other available results.