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 θ point and determine its exponents as ν=0.58±0.01, φ=0.90±0.02. We also calculate a universal quantity for the rings, which was recently determined for the θ’ point. Our results are inconsistent with the θ and θ’ points being in the same universality class.

• Received 20 July 1989

DOI:https://doi.org/10.1103/PhysRevA.41.3074