Oriented Self-Avoiding Walks with Orientation-Dependent Interactions

Abstract

We consider oriented self-avoiding walks on the square lattice with different interactions between steps depending on their relative parallel or anti-parallel orientations. We derive rigorous bounds on the free energy and prove the existence of a phase transition. By means of exact enumeration and Monte Carlo simulation, we study the phase diagram and the mean number of contacts. We show that the mean number of anti-parallel contacts increases linearly with the number of steps, while the mean number of parallel contacts asymptotically approach a constant.Key wordsSelf-avoiding walksoriented walkscollapsespiral walksMonte Carloexact enumerations