Phase structure of CP(N-1) model with topological term
  CP(N-1) model with topological term is numerically studied. The topological charge distribution P(Q) is calculated and then transformed to the partition function Z($\theta$) as a function of $\theta$ parameter. In the strong coupling region, P(Q) shows a gaussian behavior, which indicates a first order phase transition at $\theta =\pi$. In the weak coupling region,   P(Q) deviates from gaussian. A bending behavior of resulting F($\theta$) at $\theta \neq \pi$, which might be a signal of a first order phase transition, could be misled by large errors coming from the fourier transform of P(Q). Results are shown mainly for CP(3) case. 
M. Imachi, S. Kanou and H. Yoneyama