True self-avoiding walks on a percolation cluster

Abstract

The authors investigate by Monte Carlo simulations the critical behaviour of true self-avoiding walks (TSAWs) on a percolation cluster performed very close to the percolation threshold. Specifically they generate TSAWs on a site-percolated incipient 'infinite cluster', for various values of the self-avoidance parameter g)0. They found that such walks exhibit critical behaviour different from that of ordinary-self-avoiding walks and also from that of random walks of no constraint. The flory exponent obtained was v=0432+or-0.005 for all g)0, which agrees well with the Flory-type formula suggested by Rammal (1984).