On anisotropic spiral self-avoiding walks

We report on a Monte Carlo study of so-called two-choice-spiral self-avoiding walks on the square lattice. These have the property that their geometric size (such as is measured by the radius of gyration) scales anisotropically, with exponent values that seem to defy rational fraction conjectures. This polymer model was previously understood to be in a universality class different to ordinary self-avoiding walks, directed walks (which are also anisotropic), and symmetric spiral walks, in two dimensions. Our Monte Carlo study concurs with those previous exact enumeration studies in that respect. However, we estimate substantially different values for the scaling exponents associated with the geometric size of the walks. We give arguments that explain this difference in terms of a turning point in the local exponent values, and in turn explain this by arguing for the existence of probable logarithmic corrections. We also supply numerical evidence supporting a conjecture concerning the angle of anisotropy in the model.