Universality Class of $O(N)$ Models

Abstract

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 $\eta =1/4$, 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 $\theta =\pi$.

Comments: 8 pages, with 3 figures included, postscript. An error concerning the errors has been corrected