Nonzero baryon density QCD lattice simulations suffer from the well known sign problem, which has so far prevented the exploration of the QCD phase diagram. In this talk we discuss our results on the phase diagram of the 3d O(4) model. This model is an effective theory of QCD with two flavors in the chiral limit, which can be simulated at nonzero baryon density without sign problem. In this model the baryon number is represented by the topological charge. The global symmetry of this model is spontaneously broken down to O(3), which is locally isomorphic to and presumably in the same universality class as the chiral symmetry breaking in QCD with two massless quarks, SU(2)_L x SU(2)_R -> SU(2)_{L=R}. We could follow the line of the second order phase transition up to μ_B = 363 MeV and T_c = 125 MeV. At this point, we observed possible indications of a transition to first order, hence the Critical Endpoint might be near-by.

Oral