Asymptotic properties of spiral self-avoiding walks

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Abstract
The authors consider the spiral self-avoiding walk model recently introduced by Privman (1983). On the basis of an analogy with the partitioning of the integers, they argue that the number of N-step spiral walks should increase asymptotically as rho square root N with rho a constant, leading to an essential singularity in the generating function. Enumeration data to 65 terms indicates, however, that cN apparently varies as rho N alpha , with alpha approximately=0.55. They also study the N-dependence of the mean-square end-to-end distance (RN2), and of the mean rotation angle, ( theta N), for N-step walks. From series extrapolations, they estimate that (RN2) approximately N1.2, and ( theta N) approximately N0.55.

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