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 $\nu$ 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.

5 pages, 5 figures

References in corpus (4)

• Accurate estimate of the critical exponent $\nu$ for self-avoiding walks via a fast implementation of the pivot algorithm
• Multifractality of self-avoiding walks on percolation clusters
• Scaling behavior of self-avoiding walks on percolation clusters
• Walking on fractals: diffusion and self-avoiding walks on percolation clusters

Cited by in corpus (3)

• Self-avoiding walks and connective constants in clustered scale-free networks
• Scaling laws for random walks in long-range correlated disordered media
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