Fractals Meet Fractals: Self-Avoiding Random Walks on Percolation Clusters
نویسندگان
چکیده
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.
منابع مشابه
Walking on fractals: diffusion and self-avoiding walks on percolation clusters
We consider random walks (RWs) and self-avoiding walks (SAWs) on disordered lattices directly at the percolation threshold. Applying numerical simulations, we study the scaling behavior of the models on the incipient percolation cluster in space dimensions d = 2, 3, 4. Our analysis yields estimates of universal exponents, governing the scaling laws for configurational properties of RWs and SAWs...
متن کاملAnomalous random walks and di↵usions: From fractals to random media
We present results concerning the behavior of random walks and di↵usions on disordered media. Examples treated include fractals and various models of random graphs, such as percolation clusters, trees generated by branching processes, Erdős-Rényi random graphs and uniform spanning trees. As a consequence of the inhomogeneity of the underlying spaces, we observe anomalous behavior of the corresp...
متن کاملWhere two fractals meet: the scaling of a self-avoiding walk on a percolation cluster.
The scaling properties of self-avoiding walks on a d -dimensional diluted lattice at the percolation threshold are analyzed by a field-theoretical renormalization group approach. To this end we reconsider the model of Phys. Rev. Lett. 63, 2819 (1989)] and argue that via renormalization its multifractal properties are directly accessible. While the former first order perturbation did not agree w...
متن کاملLinear and Branched Polymers on Fractals
This is a pedagogical review of the subject of linear polymers on deterministic finitely ramified fractals. For these, one can determine the critical properties exactly by real-space renormalization group technique. We show how this is used to determine the critical exponents of self-avoiding walks on different fractals. The behavior of critical exponents for the n-simplex lattice in the limit ...
متن کاملRandom walks on fractals and stretched exponential relaxation.
Stretched exponential relaxation [exp-(t/tau)(beta(K))] is observed in a large variety of systems but has not been explained so far. Studying random walks on percolation clusters in curved spaces whose dimensions range from 2 to 7, we show that the relaxation is accurately a stretched exponential and is directly connected to the fractal nature of these clusters. Thus we find that in each dimens...
متن کامل