Scaling and multiscaling laws in random fuse networks

We present a numerical simulation of a random fuse network in which the thresholds of the fuses are distributed randomly. We calculate the breaking characteristics and find that they scale with the system size L with an exponent close to 0.87 in the early stages of breaking. The number of fuses burnt goes as $L^{1.7}$. Just before the system breaks fully apart, the distribution of local currents is multifractal, as opposed to the constant-gap scaling found for this distribution before the catastrophic regime sets in. Our results are remarkably stable with respect to variations of the quenched disorder in the thresholds, for which we tried power-law and Weibull distributions.