Voltage distribution in a two-component random system

A disordered medium composed of randomly arranged metal and insulator, both with finite conductance, is considered. The distribution of voltage drops upsilon in such two-component random system has been calculated both analytically and numerically. It is shown that the distribution N(y) of the logarithm of voltage drops, y=-ln(upsilon(2)), is the sum of several members, N-ck(y) and N-ik(y), k=0,1,2,....Members N-ck(y) describe the voltage distribution in the metallic phase. Members N-ik(y) describe the voltage distribution in the insulating component. The subsequent members are shifted subsequently on the y axis by an amount of 2k ln(hL(1/(nu phi))), where phi is the crossover exponent and nu is the percolation correlation length exponent. The zero-order member of the N-ck family is governed by the multifractal spectrum f(alpha), where alpha=y/lnL, found originally for the random resistor network. The zero-order member of the N-ik family is governed by the multifractal spectrum phi(alpha) found originally for the random resistor superconductor network. The next members are built from two components. The first one is the scaled repetition of N-c0 for the N-ck family or N-i0 for the N-ik family. The other one is the distribution of voltage drops in such percolation objects like dangling ends, isolated clusters for the N-ck family or clusters perimeter for the N-ik family.