Anomalous polymer collapse winding angle distributions

TL;DR

This paper investigates the winding angle distributions of polymers in two dimensions, showing Gaussian behavior at high temperatures and deviations at collapse points, with evidence of stretched exponential distributions in complex states.

Contribution

It extends previous work by analyzing interacting self-avoiding trails, revealing breakdown of Gaussian distribution at collapse points and proposing alternative models.

Findings

Gaussian winding angle distribution in high-temperature swollen state

Breakdown of Gaussian distribution at polymer collapse point

Evidence of stretched/compressed exponential distributions at low temperatures

Abstract

In two dimensions polymer collapse has been shown to be complex with multiple low temperature states and multi-critical points. Recently, strong numerical evidence has been provided for a long-standing prediction of universal scaling of winding angle distributions, where 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 . Here we extend this work by considering interacting self-avoiding trails which are believed to be a model representative of some of the more complex behaviour. We provide robust evidence that, while the high temperature swollen state of this model has a winding angle distribution that is also Gaussian, this breaks down at the polymer collapse point and at low temperatures. Moreover, we provide some evidence that the distributions are well modelled by stretched/compressed exponentials, in contradistinction to the behaviour found in interacting self-avoiding walks.