Swelling-collapse transition of self-attracting walks

We study the structural properties of self-attracting walks in d dimensions using scaling arguments and Monte Carlo simulations. We find evidence of a transition analogous to the Θ transition of polymers. Above a critical attractive interaction [Formula Presented] the walk collapses and the exponents ν and k, characterizing the scaling with time t of the mean square end-to-end distance [Formula Presented] and the average number of visited sites [Formula Presented] are universal and given by [Formula Presented] and [Formula Presented] Below [Formula Presented] the walk swells and the exponents are as with no interaction, i.e., [Formula Presented] for all d, [Formula Presented] for [Formula Presented] and [Formula Presented] for [Formula Presented] At [Formula Presented] the exponents are found to be in a different universality class.