Fractals Meet Fractals: Self-Avoiding Random Walks on Percolation Clusters

TL;DR

This paper investigates the scaling behavior of self-avoiding walks on percolation clusters across multiple dimensions, revealing a multifractal spectrum that emerges from the interaction of two fractal structures.

Contribution

It provides numerical estimates of critical exponents for SAWs on percolation clusters and demonstrates the emergence of a multifractal spectrum in this context.

Findings

Critical exponents for SAWs on percolation clusters are estimated.

A multifractal spectrum is observed when two fractals interact.

Numerical simulations confirm the complex scaling behavior across dimensions.

Abstract

The scaling behavior of linear polymers in disordered media, modelled by self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by numerical simulations. We apply the pruned-enriched Rosenbluth chain-growth method (PERM). Our numerical results yield estimates of critical exponents, governing the scaling laws of disorder averages of the configurational properties of SAWs, and clearly indicate a multifractal spectrum which emerges when two fractals meet each other.