An improved Monte Carlo renormalization-group method is used to determine the $\beta$ function of the two-dimensional O(4) $\sigma$ model. While for (inverse) couplings $\beta \gtrsim 2.2$ one obtains agreement with asymptotic scaling according to asymptotic freedom, one can see deviations from it at smaller couplings. They are, however, consistent with the behavior of the correlation length, indicating "scaling" according to the full $\beta$ function. These results contradict recent claims that the model has a critical point at finite coupling.

• Received 7 March 1988

DOI:https://doi.org/10.1103/PhysRevLett.60.2235