Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster

Details Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster

2003-12-02

arxiv.org/abs/cond-mat/0312065v1

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 2 figures

Scientific paper

10.1103/PhysRevE.70.035104

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.

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