Date of this Version
Physical Review B
The behavior of a randomly diluted network of nonlinear resistors, for each of which the voltage-current relationship is |V|=r|I|α, 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|−ζ(α). The exponent ζ(α) was evaluated for 0<α<∞ and d=2, 3, 4, 5, and 6, found to decrease monotonically from the exponent describing the minimal length, at α=0, via that of the linear resistance, at α=1, to the exponent characterizing the singly connected bonds, ξ(∞)≡1. Our results agree with known results for α=0 and α=1, also with recent results for general α at d=6-ε dimensions. The second moment 〈R2〉 was found to diverge as 〈R⟩2 (for all α and d), indicating a scaling form for the probability distribution of R.
Meir, Y., Blumenfeld, R., Aharony, A., & Harris, A. (1986). Series Analysis of Randomly Diluted Nonlinear Resistor Networks. Physical Review B, 34 (5), 3424-3428. http://dx.doi.org/10.1103/PhysRevB.34.3424
Date Posted: 12 August 2015
This document has been peer reviewed.