Spiralling directed self-avoiding walks

Abstract

A self-avoiding walk model is proposed, in which the walker performs two-choice directed self-avoiding walks while it may also make spiralling turns, and thus visiting every quarter of the plane unlimited times. The generating function for the square lattice is obtained, and an asymptotic form for the number of N-step walks, aN, is derived. The aN of the model belongs to the same universality class with the two-choice directed self-avoiding walk. However, the model achieves a higher number of N-step walks than the two-choice directed self-avoiding walk by a factor of C approximately=4.23609.