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.

arXiv comment5 pages, 5 figures

References in corpus (17)

• Self-similarity of complex networks
• A fast Monte Carlo algorithm for site or bond percolation
• Accurate estimate of the critical exponent $\nu$ for self-avoiding walks via a fast implementation of the pivot algorithm
• Simultaneous analysis of three-dimensional percolation models
• Exact enumeration of self-avoiding walks
• Multifractal behavior of linear polymers in disordered media
• Statistics of self-avoiding walks on randomly diluted lattice
• Effects of Molecular Crowding on stretching of polymers in poor solvent
• Scaling behavior of linear polymers in disordered media
• Multifractality of self-avoiding walks on percolation clusters
• 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
• Weak Non Self-Averaging Behaviour for Diffusion in a Trapping Environment
• Ising and Potts Models on Quenched Random Gravity Graphs
• Polymers in crowded environment under stretching force: globule-coil transitions
• Linear Polymers in Disordered Media - the shortest, the longest and the mean(est) SAW on percolation clusters

Cited by in corpus (7)

• Exploring different regimes in finite-size scaling of the droplet condensation-evaporation transition
• Recursive Percolation
• Scaling Analysis of Random Walks with Persistence Lengths: Application to Self-Avoiding Walks
• Self-avoiding walks and connective constants in clustered scale-free networks
• Semi-flexible compact polymers in two dimensional nonhomogeneous confinement
• Scaling laws for random walks in long-range correlated disordered media
• Polymers in disordered environments