Non-trivial θ-vacuum effects in the 2-d O(3) model

We study theta-vacua in the 2-d lattice O(3) model using the standard action and an optimized constraint action with very small cut-off effects, combined with the geometric topological charge. Remarkably, dislocation lattice artifacts do not spoil the non-trivial continuum limit at theta not equal 0, and there are different continuum theories for each value 0 <= theta <= pi. A very precise Monte Carlo study of the step scaling function indirectly confirms the exact S-matrix of the 2-d O(3) model at theta = pi.