We study the temperature dependence of conductivity for high-resistivity granular disordered systems in terms of the critical-path method. It is shown that the low-field conductivity $\exp (-\frac{A}{T^{\alpha }})$ with $\alpha =\frac{1}{2}$ is obeyed over large temperature ranges with possible crossovers to $\alpha =\frac{1}{4}$ at low temperatures and to $\alpha >\frac{1}{2}$ at high temperatures. The temperatures at which the crossovers occur depend on the distribution of grain sizes. Comparisons are made with experiments and with other theoretical approaches.

• Received 1 December 1982

DOI:https://doi.org/10.1103/PhysRevB.27.2583