SELF-AVOIDING RINGS AT THE THETA-POINT

We determine exactly the numbers C(N,m) of self-avoiding rings of N steps and m nearest-neighbor pairs, for N up to 28, on the square lattice, as well as the average squared radius of gyration for such rings. From these data we locate the point and determine its exponents as =0.58 0.01, =0.90 0.02. We also calculate a universal quantity for the rings, which was recently determined for the point. Our results are inconsistent with the and points being in the same universality class. © 1990 The American Physical Society.