Structural properties of self-attracting walks - art. no. 046117

Self-attracting walks (SATW) with attractive interaction u>0 display a swel ling-collapse transition at a critical tic for dimensions d greater than or equal to2, analogous to the Theta transition of polymers. We are intereste d in the structure of the clusters generated by SATW below u(c) (swollen wa lk), above u(c) (collapsed walk), and at u(c), which can be characterized b y the fractal dimensions of the clusters d(f) and their interface d(l). Usi ng scaling arguments and Monte Carlo simulations, we find that for u<u(c), the structures are in the universality class of clusters generated by simpl e random walks. For u > u(c), the clusters are compact, i.e., d(f)=d and d( l)=d-1. At u(c), the SATW is in a new universality class. The clusters are compact in both d = 2 and d = 3, but their interface is fractal: d(l) = 1.5 0 +/- 0.01 and 2.73 +/- 0.03 in d = 2 and d = 3, respectively. In d = 1, wh ere the walk is collapsed for all u and no swelling-collapse transition exi sts, we derive analytical expressions for the average number of visited sit es [S] and the mean time [t] to visit S sites.