CURRENT DISTRIBUTIONS IN A 2-DIMENSIONAL RANDOM-RESISTOR NETWORK

The current and logarithm-of-the-current distributions n(absolute value of i) and n(\ln absolute value of i\) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. The kth moment (-9 less-than-or-equal-to k less-than-or-equal-to 8) of n(\ln absolute value of i\) i.e., [\ln absolute value of i\k], is found to scale with the linear size L as (ln L)beta(k). The exponents beta(k) are not inconsistent with the recent theoretical prediction beta(k) = k, with deviations which may be attributed to severe finite-size effects. For small currents, ln n(y) almost-equal-to - gamma-y, yielding information on the threshold below which the multifractality of n(absolute value of i) breaks down. Our numerical results for the moments of the currents are consistent with other available results.