The winding angle of planar self-avoiding walks
- 1 August 1984
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 17 (11) , L569-L578
- https://doi.org/10.1088/0305-4470/17/11/003
Abstract
The problem of understanding the asymptotic statistical behaviour of the winding angle, theta N, of a self-avoiding walk of N steps on a planar lattice is posed. Exact series expansion data for the square lattice up to N=21 are reported. These data and Monte Carlo estimates up to NN2). The ratio ( theta N4)/( theta N2)2 appears to approach a limit of 2.9 to 3.2, which is close to the Gaussian value, 3. Heuristic scaling arguments are consistent with simple logarithmic growth (and also illuminate the logarithmic behaviour known rigorously for free Brownian motion).Keywords
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