Endpoint distribution of self-avoiding walks

Abstract

The dimerization algorithm for the generation of self‐avoiding walks was modified to generate a large number of walks with a relatively large endpoint separation. Walks of up to 512 steps were generated on the square and cubic lattices using this modified algorithm. From these walks the distribution of endpoint x coordinates of self‐avoiding walks was accurately determined over a much wider range than would be possible using earlier techniques. The distributions obtained were found to be in general agreement with those proposed earlier for shorter walks by Domb, Gillis, and Wilmers.