  We study the structural properties of self-attracting walks in d dimensions
using scaling arguments and Monte Carlo simulations. We find evidence for a
transition analogous to the \Theta transition of polymers. Above a critical
attractive interaction u_c, the walk collapses and the exponents \nu and k,
characterising the scaling with time t of the mean square end-to-end distance
<R^2> ~ t^{2 \nu} and the average number of visited sites <S> ~ t^k, are
universal and given by \nu=1/(d+1) and k=d/(d+1). Below u_c, the walk swells
and the exponents are as with no interaction, i.e. \nu=1/2 for all d, k=1/2 for
d=1 and k=1 for d >= 2. At u_c, the exponents are found to be in a different
universality class.

Condensed Matter