Department of Physics Papers

Document Type

Journal Article

Date of this Version

9-1-1987

Publication Source

Physical Review B

Volume

36

Issue

7

Start Page

3950

Last Page

3952

DOI

10.1103/PhysRevB.36.3950

Abstract

The behavior of randomly diluted networks of nonlinear resistors, for each of which the voltage-current relationship is |V|=r|I|α, where α is negative, is studied using low-concentration series expansions on d-dimensional hypercubic lattices. The average nonlinear resistance ⟨R⟩ between a pair of points on the same cluster, a distance r apart, scales as rζ(α)/ν, where ν is the correlation-length exponent for percolation, and we have estimated ζ(α) in the range −1≤α≤0 for 1≤d≤6. ζ(α) is discontinuous at α=0 but, for α<0, ζ(α) is shown to vary continuously from ζmax, which describes the scaling of the maximal self-avoiding-walk length (for α→0−), to ζBB, which describes the scaling of the backbone (at α=−1). As α becomes large and negative, the loops play a more important role, and our series results are less conclusive.

Comments

At the time of publication, author A. Brooks Harris was affiliated with Tel Aviv University, Tel Aviv, Israel. Currently, he is a faculty member in the Physics Department at the University of Pennsylvania.

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Date Posted: 12 August 2015

This document has been peer reviewed.