Multifractality of self-avoiding walks on percolation clusters

TL;DR

This paper investigates the multifractal properties of self-avoiding walks on percolation cluster backbones across multiple dimensions, revealing a spectrum of singularities and estimating critical exponents through simulations and theoretical expansion.

Contribution

It introduces a comprehensive numerical analysis of the multifractal spectrum of SAWs on percolation clusters and aligns these findings with field-theoretical predictions.

Findings

Multifractal spectrum of singularities identified in SAWs on percolation clusters

Critical exponents for higher moments estimated with good agreement to theory

Numerical simulations confirm theoretical xpansion predictions

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)).