Scaling behavior of self-avoiding walks on percolation clusters

TL;DR

This paper investigates how self-avoiding walks behave on percolation cluster backbones across multiple dimensions using Monte Carlo simulations, providing estimates of critical exponents and discussing finite-size effects.

Contribution

It introduces numerical estimates of critical exponents for SAWs on percolation clusters in multiple dimensions using advanced Monte Carlo methods.

Findings

Estimated critical exponents for SAWs on percolation clusters

Analysis of finite-size scaling effects

Insights into the dimensional dependence of scaling laws

Abstract

The scaling behavior of self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by Monte Carlo simulations. We apply the pruned-enriched Rosenbluth chain-growth method (PERM). Our numerical results bring about the estimates of critical exponents, governing the scaling laws of disorder averages of the end-to-end distance of SAW configurations. The effects of finite-size scaling are discussed as well.