Fractals Meet Fractals: Self-Avoiding Random Walks on Percolation Clusters

The scaling behavior of linear polymers in disordered media, modelled by self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by numerical simulations. We apply the pruned-enriched Rosenbluth chain-growth method (PERM). Our numerical results yield estimates of critical exponents, governing the scaling laws of disorder averages of the configurational properties of SAWs, and clearly indicate a multifractal spectrum which emerges when two fractals meet each other.