Winding angles for two-dimensional polymers with orientation dependent interactions

TL;DR

This paper investigates the winding angles of two-dimensional oriented polymers with orientation-dependent interactions, revealing universal behavior and phase transition characteristics through analytical and simulation methods.

Contribution

It provides the first comprehensive analysis of winding angle variance in such polymers, identifying phase boundaries and the nature of phase transitions.

Findings

Winding angle distribution is universal across phases.

The $ heta$--point marks the meeting of three phase boundaries.

Transition between collapsed phases is continuous.

Abstract

We study winding angles of oriented polymers with orientation-dependent interaction in two dimensions. Using exact analytical calculations, computer simulations, and phenomenological arguments, we succeed in finding the variance of the winding angle for most of the phase diagram. Our results suggest that the winding angle distribution is a universal quantity, and that the $\theta$--point is the point where the three phase boundaries between the swollen, the normal collapsed, and the spiral collapsed phase meet. The transition between the normal collapsed phase and the spiral phase is shown to be continuous.