Multifractal properties of the random resistor network

We study the multifractal spectrum of the current in the two-dimensional ra ndom resistor network at the percolation threshold. We consider two ways of applying the voltage difference: (i) two parallel bars, and (ii) two point s. Our numerical results suggest that in the infinite system limit, the pro bability distribution behaves for small i as P(i)similar to 1/i, where i is the current. As a consequence, the moments of i of order q less than or eq ual to q(c)=0 do not exist and all currents of value below the most probabl e one have the fractal dimension of the backbone. The backbone can thus be described in terms of only (i) blobs of fractal dimension d(B) and (ii) hig h current carrying bonds of fractal dimension going from 1/v to d(B).