Critical behavior of CP1 at theta=pi, Haldane's conjecture, and the relevant universality class

Using an approach to analyze the $\theta$ dependence of systems with a $\theta$ term we recently proposed, the critical behavior of CP^1 at $\theta=\pi$ is studied. We find a region outside the strong coupling regime where Haldane’s conjecture is verified. The critical line, however, does not belong to the universality class of the Wess-Zumino-Novikov-Witten model at topological coupling k = 1 since it shows continuously varying critical exponents.