Self-avoiding walks on percolation clusters

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Abstract
The author studies self-avoiding walks (SAWs) on percolation clusters. A scaling function representation for R, the mean end-to-end distance, is proposed which describes a crossover from ordinary SAWs to SAWs on fractals. He distinguishes between SAWs on a single cluster for which R approximately Nx, where x= nu 1, and SAWs on all clusters for which R approximately Nz, where z= nu 2 and N is the number of monomers in the walk. He estimates nu 1(d=2) approximately=1.285 and the correction-to-scaling exponent Omega (d=2) approximately=1.3, and nu 1(d=3) approximately=1.38. Two plausible generalisations of the Flory (1953) approximation for nu 1 are investigated and it is argued that none of them provides a satisfactory approximation for nu 1 at all dimensions.

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