Numerical study of the mass spectrum in the 2D O(3) sigma model with a theta term

It has been conjectured that the mass spectrum of the O(3) non–linear sigma model with a \theta term in 2 dimensions may possess an excited state, which decays when theta is lowered fromp below a critical value. Since the direct numerical investigation of the model is prevented by a sign problem, we try to infer some information on the mass spectrum at real \theta by studying the model at imaginary \theta via analytic continuation. A modified Swendsen–Wang cluster algorithm has been introduced to simulate the model with the \theta term.