Winding angle distributions for two-dimensional collapsing polymers

TL;DR

This paper provides numerical evidence supporting the universal scaling law of winding angle distributions in two-dimensional collapsing polymers, confirming theoretical predictions across different phases.

Contribution

It offers the first numerical validation of the universal Gaussian winding angle distribution with specific variance growth in various phases of collapsing polymers.

Findings

Winding angle distribution is Gaussian with variance proportional to log N.

Confirmed C=2 in swollen phase, C=24/7 at θ-point, and C=4 in collapsed phase.

Supports theoretical predictions across different polymer phases.

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.