Walking on fractals: diffusion and self-avoiding walks on percolation clusters

TL;DR

This paper investigates the scaling behavior of random walks and self-avoiding walks on percolation clusters at the threshold, providing universal exponents across different spatial dimensions through numerical simulations.

Contribution

It offers new estimates of universal exponents for RWs and SAWs on percolation clusters in multiple dimensions, advancing understanding of disordered lattice models.

Findings

Universal exponents for RWs and SAWs estimated in 2, 3, 4 dimensions

Scaling laws for configurational properties characterized

Numerical simulations confirm theoretical predictions

Abstract

We consider random walks (RWs) and self-avoiding walks (SAWs) on disordered lattices directly at the percolation threshold. Applying numerical simulations, we study the scaling behavior of the models on the incipient percolation cluster in space dimensions d=2, 3, 4. Our analysis yields estimates of universal exponents, governing the scaling laws for configurational properties of RWs and SAWs.