COLLAPSE TRANSITION OF SELF-AVOIDING WALKS ON A SQUARE LATTICE IN THEBULK AND NEAR A LINEAR WALL - THE UNIVERSALITY CLASSES OF THE THETA AND THETA' POINTS

Using the scanning method we study by extensive simulations the theta transition of self-avoiding walks with nearest-neighbor attractions in the bulk and near a linear wall on a square lattice. Consistent resul ts for the two models are obtained for the radius of gyration, but not for the end-to-end distance. Our results for the exponents nu and gam ma agree with those derived by Duplantier and Saleur [Phys. Rev. Lett. 59, 539 (1987)] for the theta' model. However, our results for the cr ossover exponent phi (which constitute upper bounds for the correct va lue) are significantly-larger than the value of phi(theta'). At the or dinary point our result for gamma1 is larger (even though not much) th an the value suggested by Vanderzande, Stella, and Seno [Phys. Rev. Le tt. 67, 2757 (1991)] for the theta' model.