ac Hopping Conduction at Extreme Disorder Takes Place on the Percolating Cluster

Simulations of the random barrier model show that ac currents at extreme disorder are carried almost entirely by the percolating cluster slightly above threshold; thus contributions from isolated low-activation-energy clusters are negligible. The effective medium approximation in conjunction with the Alexander-Orbach conjecture lead to an excellent analytical fit to the universal ac conductivity with no nontrivial fitting parameters.