Winding angle distributions for two-dimensional collapsing polymers

Abstract

We provide numerical support for a long-standing prediction of universal scaling of winding angle distributions. Simulations of interacting self-avoiding walks show that the winding angle distribution for $N$-step walks is compatible with the theoretical prediction of a Gaussian with a variance growing asymptotically as $C\log N$, with $C=2$ in the swollen phase (previously verified), and $C=24/7$ at the $\theta$-point. At low temperatures weaker evidence demonstrates compatibility with the same scaling and a value of $C=4$ in the collapsed phase, also as theoretically predicted.