PERCOLATION AND CONDUCTIVITY IN NEARLY-1D SYSTEMS

A polymer network is treated as an anisotropic fractal with fractional dimensionality D = 1 + epsilon close to one. The percolation model on such a fractal is studied. Using the real space renormalization group approach of Migdal and Kadanoff we find the threshold value and all t he critical exponents in the percolation model to be strongly nonanaly tic functions of epsilon, e.g. the critical exponent of tile conductiv ity was obtained to be epsilon(-2) exp (-1 - 1/epsilon). The main part of the finite size conductivity distribution function at the threshol d was found to be universal if expressed in terms: of the fluctuating variable which is proportional to a large power of the conductivity, b ut with epsilon-dependent low-conductivity cut-off. Its reduced centra l momenta are of the order of e(-1/epsilon) lip to very high orders.