  We report the results of a Monte Carlo study of the continuum limit of the
two dimensional O(3) non-linear $\sigma$ model. The notable finding is that it
agrees very well with both the prediction inspired by Zamolodchikovs' S-matrix
ansatz and with the continuum limit of the dodecahedron spin model. The latter
finding renders the existence of asymptotic freedom in the O(3) model rather
unlikely.
