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Simulations of the random barrier model show that ac currents at extremedisorder are carried almost entirely by the percolating cluster slightly abovethreshold; thus contradicting traditional theories contributions from isolatedlow-activation-energy clusters are negligible. The effective mediumapproximation in conjunction with the Alexander-Orbach conjecture leads to anexcellent analytical fit to the universal ac conductivity with no nontrivialfitting parameters.

Ac hopping conduction at extreme disorder takes place on the percolating cluster