The location of the up to now hypothetical critical endpoint and the exploration of the QCD phase diagram are important challenges in both theoretical and experimental physics. With two massless quark flavors the QCD Lagrangian has a $SU(2)_L \times SU(2)_R = O(4)$ symmetry. This symmetry is isomorphic to the one of the four component Heisenberg ferromagnet which we use as an effective model. With massive quarks, this symmetry breaks explicitly down to $SU(2) = O(3)$, hence a degenerate quark mass is equivalent to an external magnetic field in the effective model. We present our results from the numerical simulations of the 3d O(4) Heisenberg ferromagnet with an external magnetic field, where the topological charge represents the baryon number. This is used as an effective model that avoids the notorious sign problem which has prevented numerical QCD simulations at high baryon density. We plot the conjectured QCD phase diagram monitoring the crossover for a chemical potential between 0 MeV to 250 MeV. However, we did not observe the critical endpoint in this range of chemical potentials.

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