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Long linear polymers in strongly disordered media are well described byself-avoiding walks (SAWs) on percolation clusters. The length-distribution ofthese SAWs encompasses to distinct averages, viz. the averages over cluster-and SAW-conformations. For the latter average, there are two basic options, onebeing static and one being kinetic. It is well known for static averaging thatif the disorder of the underlying medium is weak, differences to the orderedcase appear merely in non-universal quantities. Using dynamical field theory,we show that the same holds true for kinetic averaging. For strong disorder,i.e., the medium being close to the percolation point, we employ a field theoryfor the nonlinear random resistor network in conjunction with a real-worldinterpretation of Feynman diagrams, and we calculate the scaling exponents forthe shortest, the longest and the mean or average SAW to 2-loop order. Inaddition, we calculate to 2-loop order the entire family of multifractalexponents that governs the moments of the the statistical weights of theelementary constituents (bonds or sites of the underlying fractal cluster)contributing to the SAWs. Our RG analysis reveals that kinetic averaging leadsto renormalizability whereas static averaging does not, and hence, we arguethat the latter does not lead to a well-defined scaling limit. We discuss thepossible implications of this finding for experiments and numerical simulationswhich have produced wide-spread results for the exponent of the average SAW. Tocorroborate our results, we also study the well-known Meir-Harris model forSAWs on percolation clusters. We demonstrate that this model leads back to2-loop order to the renormalizable real world formulation with kineticaveraging if the replica limit is consistently performed at the first possibleinstant of the calculation.

Linear Polymers in Disordered Media - the shortest, the longest and the mean(est) SAW on percolation clusters