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 of its field configurations. 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$)_L$ ⊗ SU(2$)_R$ → SU(2$)_{L=R}$. At vanishing $μ_B$ we obtain the critical temperature $T_c$ = 154.6(4) MeV, consistent with previous lattice studies. 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. We did not find solid evidence for any $μ_B$-dependence of the critical exponents.

Theory and Phenomenology