Anomalous polymer collapse winding angle distributions

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.

9 pages, 7 figures

References in corpus (4)

• Geometrical Properties of Two-Dimensional Interacting Self-Avoiding Walks at the Theta-Point
• Collapse transition of self-avoiding trails on the square lattice
• Identification of a polymer growth process with an equilibrium multi-critical collapse phase transition: the meeting point of swollen, collapsed and crystalline polymers
• Winding angle distributions for two-dimensional collapsing polymers