Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster
arXiv:cond-mat/0312065 · doi:10.1103/PhysRevE.70.035104
Abstract
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 Y. Meir and A. B. Harris (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 with the results of other methods, we find that the asymptotic behavior of a self-avoiding walk on the percolation cluster is governed by the exponent nu_p=1/2 + epsilon/42 + 110epsilon^2/21^3, epsilon=6-d. This analytic result gives an accurate numeric description of the available MC and exact enumeration data in a wide range of dimensions 2<=d<=6.
4 pages, 2 figures
References in corpus (1)
Cited by in corpus (16)
- Public transport networks: empirical analysis and modeling
- Network Harness: Metropolis Public Transport
- 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
- Walking on fractals: diffusion and self-avoiding walks on percolation clusters
- Shapes of macromolecules in good solvents: field theoretical renormalization group approach
- Entropy-induced separation of star polymers in porous media
- Recursive Percolation
- Fractals Meet Fractals: Self-Avoiding Random Walks on Percolation Clusters
- Asymptotic scaling behavior of self-avoiding walks on critical percolation clusters
- Polymers in crowded environment under stretching force: globule-coil transitions
- Self-Avoiding Walk on the square site-diluted Ising-correlated lattice
- 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