Theta-point polymers in the plane and Schramm-Loewner evolution

We study the connection between polymers at the \u3b8 temperature on the lattice and Schramm-Loewner chains with constant step length in the continuum. The second of these realize a useful algorithm for the exact sampling of tricritical polymers, where finite-chain effects are excluded. The driving function computed from the lattice model via a radial implementation of the zipper method is shown to converge to Brownian motion of diffusivity \u3ba=6 for large times. The distribution function of an internal portion of walk is well approximated by that obtained from Schramm-Loewner chains. The exponent of the correlation length \u3bd and the leading correction-to-scaling exponent \u3941 measured in the continuum are compatible with \u3bd=4/7 (predicted for the \u3b8 point) and \u3941=72/91 (predicted for percolation). Finally, we compute the shape factor and the asphericity of the chains, finding surprising accord with the \u3b8-point end-to-end values