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

We study the connection between polymers at the θ 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 κ=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 ν and the leading correction-to-scaling exponent Δ1 measured in the continuum are compatible with ν=4/7 (predicted for the θ point) and Δ1=72/91 (predicted for percolation). Finally, we compute the shape factor and the asphericity of the chains, finding surprising accord with the θ-point end-to-end values.