  We discuss the Heisenberg model and its chiral extension in an extended
truncation with the help of functional methods. Employing computer algebra to
derive the beta functions, and pseudo-spectral methods to solve them, we are
able to go significantly beyond earlier approximations, and provide new
estimates on the critical quantities of both models. The fixed point of the
Heisenberg model is mostly understood, and our results are in agreement with
estimates from various other approaches, including Monte Carlo and conformal
bootstrap studies. By contrast, in the chiral case, the formerly known
disagreement with lattice studies persists, raising the question whether
actually the same universality class is described.
