Department of Physics Papers

Document Type

Journal Article

Date of this Version

4-1-1987

Publication Source

Physical Review B

Volume

35

Issue

10

Start Page

5048

Last Page

5055

DOI

10.1103/PhysRevB.35.5048

Abstract

We consider the critical properties of the two-point resistance and its fluctuations due to microscopic noise in a randomly diluted resistor network near the percolation threshold pc. We introduce a n×m replicated Hamiltonian in order to treat separately the configuration average over the randomly occupied bonds denoted [ ]av and the average over probability distribution function of the fluctuating microscopic bond conductance, denoted { }f. We evaluate a family of exponents {ψl} (l=2,3,. . .) whose values are 1+O(ε) with ε=6-d where d is the spatial dimensionality. Each ψl governs the critical behavior of the lth cumulant of the resistance between the sites x,x’ conditionally averaged subject to the sites being in the same cluster such that C¯R (l)(x,x’)~‖x-x'‖ψl/vp for p near pc, where νp is the correlation-length exponent for percolation. Furthermore, ψ2=1+ε/105 determines the dependence of the variance of the resistance in a finite network on size L as Lψ2/vp.

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Date Posted: 12 August 2015

This document has been peer reviewed.