Winding angles for two-dimensional polymers with orientation-dependent interactions

We study winding angles of oriented polymers with an 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 phases meet. The transition between the normal collapsed phase and the spiral phase is argued to be continuous.