Multifractality of self-avoiding walks on percolation clusters

Details Multifractality of self-avoiding walks on percolation clusters Multifractality of self-avoiding walks on percolation clusters

2008-07-23

arxiv.org/abs/0807.3749v1

Phys. Rev. Lett. 101, (2008) 125701

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages

Scientific paper

10.1103/PhysRevLett.101.125701

We consider self-avoiding walks (SAWs) on the backbone of percolation clusters in space dimensions d=2, 3, 4. Applying numerical simulations, we show that the whole multifractal spectrum of singularities emerges in exploring the peculiarities of the model. We obtain estimates for the set of critical exponents, that govern scaling laws of higher moments of the distribution of percolation cluster sites visited by SAWs, in a good correspondence with an appropriately summed field-theoretical \varepsilon=6-d-expansion (H.-K. Janssen and O. Stenull, Phys. Rev. E 75, 020801(R) (2007)).

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