Collapse transition of self-avoiding walks on a square lattice in the bulk and near a linear wall: The universality classes of the θ and θ' points

Using the scanning method we study by extensive simulations the θ transition of self-avoiding walks with nearest-neighbor attractions in the bulk and near a linear wall on a square lattice. Consistent results for the two models are obtained for the radius of gyration, but not for the end-to-end distance. Our results for the exponents ν and γ agree with those derived by Duplantier and Saleur [Phys. Rev. Lett. 59, 539 (1987)] for the θ' model. However, our results for the crossover exponent φ (which constitute upper bounds for the correct value) are significantly larger than the value of φ(θ'). At the ordinary point our result for γ1 is larger (even though not much) than the value suggested by Vanderzande, Stella, and Seno [Phys. Rev. Lett. 67, 2757 (1991)] for the θ' model.