The typical number of self-avoiding walks on randomly diluted lattices

Abstract

We investigate the typical number of self-avoiding walks on a randomly diluted lattice using rigorous inequalities, exact enumerations of all walks, scaling and Lifshitz arguments. We determine the critical temperature of these walks as a function of occupation probability p. We find a <<transition>> in the geometry of the clusters governing the behaviour of typical walks from <<fully occupied sphere>> to <<self-avoiding walk>>-like.