  We report the results of a very high statistics Monte Carlo study of the
continuum limit of the two dimensional O(3) non-linear $\sigma$ model. We find
a significant discrepancy between the continuum extrapolation of our data and
the form factor prediction of Balog and Niedermaier, inspired by the
Zamolodchikovs' S-matrix ansatz. On the other hand our results for the O(3) and
the dodecahedron model are consistent with our earlier finding that the two
models possess the same continuum limit.
