Series analysis of randomly diluted nonlinear resistor networks

The behavior of a randomly diluted network of nonlinear resistors, for each of which the voltage-current relationship is V=rI±, is studied with use of series expansions in the concentration p of conducting bonds on d-dimensional hypercubic lattices. The average nonlinear resistance R between pairs of sites separated by the percolation correlation length, scales as p-pc-(±). The exponent (±) was evaluated for 0<±< and d=2, 3, 4, 5, and 6, found to decrease monotonically from the exponent describing the minimal length, at ±=0, via that of the linear resistance, at ±=1, to the exponent characterizing the singly connected bonds, 3/4(z)1. Our results agree with known results for ±=0 and ±=1, also with recent results for general ± at d=6- dimensions. The second moment R2 was found to diverge as R2 (for all ± and d), indicating a scaling form for the probability distribution of R.