Current distributions in a two-dimensional random-resistor network

The current and logarithm-of-the-current distributions n({divides}i{divides}) and n({divides}ln {divides}i{divides}{divides}) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. The k th moment (-9≤k≤8) of n({divides}ln {divides}i{divides}{divides}) i.e., 〈{divides}ln {divides}i&{divides}{divides}^k〉, is found to scale with the linear size L as (In L)^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 {Mathematical expression}({divides}i{divides}) breaks down. Our numerical results for the moments of the currents are consistent with other available results.