title: Asymptotic scaling behavior of self-avoiding walks on critical percolation clusters.
abstract: We study self-avoiding walks on three-dimensional critical percolation clusters using a new exact enumeration method. It overcomes the exponential increase in computation time by exploiting the clusters' fractal nature. We enumerate walks of over 10^{4} steps, far more than has ever been possible. The scaling exponent ν for the end-to-end distance turns out to be smaller than previously thought and appears to be the same on the backbones as on full clusters. We find strong evidence against the widely assumed scaling law for the number of conformations and propose an alternative, which perfectly fits our data.
authors.affiliation: Institut für Theoretische Physik and Centre for Theoretical Sciences (NTZ), Universität Leipzig, Postfach 100920, D-04009 Leipzig, Germany.
authors.forename: Niklas
authors.initials: N
authors.lastname: Fricke
authors.affiliation: Institut für Theoretische Physik and Centre for Theoretical Sciences (NTZ), Universität Leipzig, Postfach 100920, D-04009 Leipzig, Germany.
authors.forename: Wolfhard
authors.initials: W
authors.lastname: Janke
mesh_terms: D017709:Fractals; D008956:Models, Chemical; D009010:Monte Carlo Method; D011108:Polymers / Q000737:chemistry
chemical_list: D011108:Polymers