Department of Physics Papers

Document Type

Journal Article

Date of this Version

9-1-1986

Publication Source

Physical Review B

Volume

34

Issue

5

Start Page

3424

Last Page

3428

DOI

10.1103/PhysRevB.34.3424

Abstract

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.

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Date Posted: 12 August 2015

This document has been peer reviewed.