The growing self avoiding walk

Abstract

The authors introduce a new self avoiding walk with one step probabilities which depend on the local environment. As a consequence this walk is irreversible and models the growth process of a linear polymer in a good solvent. To calculate its properties they have performed exact enumerations up to 22 steps on the square lattice and on the diamond lattice. This gives for the critical indices the values v=0.68, gamma =1.16 in two dimensions and v=0.525 and gamma >1 in three dimensions.