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We investigate the continuum limit of the step scaling function in the 2-dO(3) model with different theta-vacua. Since we find a different continuumvalue of the step scaling function for each value of theta, we can concludethat theta indeed is a relevant parameter of the theory and does not getrenormalized non-perturbatively. Furthermore, we confirm the result of theconjectured exact S-matrix theory, which predicts the continuum value at theta= pi. To obtain high precision data, we use a modified Hasenbusch improvedestimator and an action with an optimized constraint, which has very smallcut-off effects. The optimized constraint action combines the standard actionof the 2-d O(3) model with a topological action. The topological actionconstrains the angle between neighboring spins and is therefore invariantagainst small deformations of the field.

Study of theta-Vacua in the 2-d O(3) Model