Behavior near $\theta=\pi$ of the mass gap in the 2D O(3) non-linear   sigma model
  The validity of the Haldane's conjecture entails that the mass gap of the 2-dimensional O(3) non-linear sigma model with a $\theta$-term must tend to zero as $\theta$ approaches the value $\pi$ by following a precise law. In the present paper we extract the related critical exponents by simulating the model at imaginary $\theta$. 
B. Alles, M. Giordano, A. Papa
hep-lat cond-mat.stat-mech hep-th