Swelling-collapse transition of self-attracting walks

We study the structural properties of self-attracting walks in cl dimension s using scaling arguments and Monte Carlo simulations. We find evidence of a transition analogous to the Theta transition of polymers. Above a critica l attractive interaction u(c), the walk collapses and the exponents v and k , characterizing the scaling with time t of the mean square end-to-end dist ance [R-2]similar to t(2v) and the average number of visited sites [S]simil ar to t(k), are universal and given by v= 1/(d + 1) and k = d/(d+ 1). Below u(c), the walk swells and the exponents are as with no interaction, i.e., v= 1/2 for all d, k=1/2 for d=1 and k=1 for d greater than or equal to 2. A t u(c), the exponents are found to be in a different universality class.