Department of Physics Papers

Document Type

Journal Article

Date of this Version

8-20-1984

Publication Source

Physical Review Letters

Volume

53

Issue

8

Start Page

743

Last Page

746

DOI

10.1103/PhysRevLett.53.743

Abstract

We present a reanalysis of the renormalization-group calculation to first order in ε=6−d, where d is the spatial dimensionality, of the exponent, t, which describes the behavior of the conductivity of a percolating network at the percolation threshold. If we set t=(d−2)νp+ζ, where νp is the correlation-length exponent, then our result is ζ=1+(ε/42). This result clarifies several previously paradoxical results concerning resistor networks and shows that the Alexander-Orbach relation breaks down at order ε.

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Date Posted: 20 August 2015

This document has been peer reviewed.