Date of this Version
Physical Review Letters
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.
Harris, A., Kim, S., & Lubensky, T. C. (1984). ε Expansion for the Conductivity of a Random Resistor Network. Physical Review Letters, 53 (8), 743-746. http://dx.doi.org/10.1103/PhysRevLett.53.743
Date Posted: 20 August 2015
This document has been peer reviewed.