Universality Class of $O(N)$ Models

We point out that existing numerical data on the correlation length and magnetic susceptibility suggest that the two dimensional $O(3)$ model with standard action has critical exponent $\eta =1\mathrm{/}4$, which is inconsistent with asymptotic freedom. This value of $\eta$ is also different from the one of the Wess-Zumino-Novikov-Witten model that is supposed to correspond to the $O(3)$ model at $\theta =\pi$.