Critical Behavior of CP¹ at theta = pi, Haldane's Conjecture and the 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.