The end-point distribution of self-avoiding walks on a crystal lattice. II. Loose-packed lattices

Abstract

A study is made of the mean-square lengths of self-avoiding walks on a number of loose-packed lattices. It is found that the even-odd oscillations characteristic of this type of lattice may be largely removed by the use of an Euler transformation. From an analysis of the transformed series and of other moments from 1 to 10 of the distribution the mean-square length indices are estimated as gamma =1.500+or-0.005 in two dimensions and gamma =1.20+or-0.02 in three dimensions. These estimates are in good agreement with the exact simple fractions 3/2 and 6/5 favoured by several workers.