ON ANISOTROPIC SPIRAL SELF-AVOIDING WALKS

We report on a Monte Carlo study of so-called two-choice-spiral self-a voiding walks on the square lattice. These have the property that thei r geometric size (such as is measured by the radius of gyration) scale s anisotropically, with exponent values that seem to defy rational fra ction conjectures. This polymer model was previously understood to be in a universality class different to ordinary self-avoiding walks, dir ected walks (which are also anisotropic), and symmetric spiral walks, in two dimensions. Our Monte Carlo study concurs with those previous e xact enumeration studies in that respect However, we estimate substant ially different values for the scaling exponents associated with the g eometric size of the walks. We give arguments that explain this differ ence 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 conjectur e concerning the angle of anisotropy in the model.