Self-avoiding walks on percolation clusters

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 N x , where x= nu 1 , and SAWs on all clusters for which R approximately N z , 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.