Abstract
Random walks on self-avoiding walks (SAWs) are studied using Monte Carlo techniques on a square lattice (with nearest-neighbour hopping along the chain and between SAW points which are nearest neighbours on the embedding lattice). The average of the square of the end-to-end distance for random walks of t steps on SAWs of length N is fitted to the scaling forms (Rt2) varies as Ndelta tk (for t or approximately=Ntheta ), where theta approximately=2 nu s/k; nu s being the average end-to-end distance exponent for SAWs. The observed value of the exponent delta is supported by the authors' real space renormalisation group result for the conductivity of SAW chains. The exponent k has been related to the 'effective' fractal dimension of the SAW chain.
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