Multifractality of self-avoiding walks on percolation clusters

Abstract

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)).

4 pages

References in corpus (3)

• Multifractal statistics of Lagrangian velocity and acceleration in turbulence
• Exact relations between multifractal exponents at the Anderson transition
• Scaling behavior of self-avoiding walks on percolation clusters