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

Abstract

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.

5 pages, to appear in Proceedings of "Computer Simulations in Condensed Matter Physics XXII", eds. D.P. Landau, S.P. Lewis, and H.-B. Schumltler, The Procedia: Physics Procedia (in print)

References in corpus (8)

• Multifractal statistics of Lagrangian velocity and acceleration in turbulence
• Exact relations between multifractal exponents at the Anderson transition
• Multicanonical Chain Growth Algorithm
• Multifractality of self-avoiding walks on percolation clusters
• Scaling behavior of linear polymers in disordered media
• Scaling behavior of self-avoiding walks on percolation clusters
• Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster
• Walking on fractals: diffusion and self-avoiding walks on percolation clusters

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• Scaling exponents for a monkey on a tree - fractal dimensions of randomly branched polymers
• Linear Polymers in Disordered Media - the shortest, the longest and the mean(est) SAW on percolation clusters
• Scaling laws for random walks in long-range correlated disordered media
• Polymers in disordered environments
• Multifractal scaling of flux penetration in the Iron-based Superconductor Ba(Fe${}_{0.93}$Co${}_{0.07}$)${}_2$As${}_2$
• DNA thermal denaturation by polymer field theory approach: effects of the environment