Harris, A. BrooksLubensky, Tom C.Kim, Soobang2023-05-232023-05-231984-08-202015-08-13https://repository.upenn.edu/handle/20.500.14332/43209We 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.PhysicsArticle