CRITICAL PERCOLATION AND TRANSPORT IN NEARLY ONE-DIMENSION

A random hopping on a fractal network with dimension slightly above 1, d = 1 + epsilon, is considered as a model of transport for conducting polymers with nonmetallic conductivity. Within the real space renorma lization group method of Migdal and Kadanoff, the critical behavior ne ar the percolation threshold is studied. In contrast to a conventional regular expansion in epsilon, the critical indices of correlation len gth, v = epsilon(-1) + O(e(-1/epsilon)), and of conductivity, t simila r or equal to epsilon(-2) exp(-1 - 1/epsilon), are found to be nonanal ytic functions of epsilon as epsilon --> 0. In the case of variable ra nge hopping a ''1D Mott's law'' exp[-(T-t/T)(1/2)] dependence was foun d for the dc conductivity. It is shown chat the same type of strong te mperature dependence is valid for the dielectric constant and the freq uency-dependent conductivity, in agreement with experimental data for poorly conducting polymers.