Statistics of self-avoiding walks on random lattices

Abstract

The statistics of directed self-avoiding walks (SAWs) on randomly bond diluted square lattices have been solved exactly and a computer simulation study of the statistics of ordinary SAWs on diluted square lattices has also been performed. The configurational averaging has been performed here over the logarithms of the distribution functions. We find that the critical behaviour remains unchanged below a certain dilution concentrationp *, dependent on the length of the chains considered (p *=0 forN→∞), and a crossover to a higher order critical behaviour occurs beyond that point.