Resistance fluctuation at the mobility edge

Abstract

Following a Migdal-Kadanoff-type bond moving procedure, we derive the renormalization 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, K1 the mean resistance and K2 the mean square deviation of resistance exhibit a mobility edge dominated by large dispersion, i.e., K $ ’ ~ / K=, 1, suggesting inadequacy of the one-parameter scaling ansatz.