Resistance fluctuation at the mobility edge

Following a Migdal-Kadanoff-type bond moving procedure, the authors derive the renormalisation-group equations for the characteristic function of the full probability distribution of resistance (conductance) of a three-dimensional disordered system. The resulting recursion relations for the first two cumulants, κ₁ the mean resistance and κ₂, the mean-square deviation of resistance exhibit a mobility edge dominated by large dispersion, i.e. κ₂^1/2/κ₁ ≃ 1, suggesting inadequacy of the one-parameter scaling ansatz.