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Non-trivial θ-Vacuum Effects in the 2-d O(3) Model

We study θ-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 θ non-zero, and there are different continuum theories for each value of θ. 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 θ= π.