APPROXIMATE POWER-LAW CONDUCTIVITY IN THE MULTIPLE-HOPPING REGIME

Application of percolation theory to the ac conductivity, sigma(omega), of disordered systems requires a description of the microscopic transitions dominating the response at any particular frequency. These are pair relaxation at high frequencies, small clusters at intermediate frequencies (treated in a renormalized version of pair relaxation) and large clusters at low frequencies, below the loss peak. Recent results giving a quantitative representation of the frequency, omega(0), defining the crossover between pair and small cluster relaxation are applied to a quantitative calculation of the power, s, of omega in sigma(omega) just above the loss peak in the multiple-hopping regime.