Date of this Version
Physical Review B
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.
Meir, Y., Blumenfeld, R., Harris, A., & Aharony, A. (1987). Series Analysis of Randomly Diluted Nonlinear Networks With Negative Nonlinearity Exponent. Physical Review B, 36 (7), 3950-3952. http://dx.doi.org/10.1103/PhysRevB.36.3950
Date Posted: 12 August 2015
This document has been peer reviewed.