Two different matrix models for QCD with a non-vanishing quark chemical potential are shown to be equivalent by mapping the corresponding partition functions. The equivalence holds in the phase with broken chiral symmetry. It is exact in the limit of weak non-Hermiticity, where the chemical potential squared is rescaled with the volume. At strong non-Hermiticity it holds only for small chemical potential. The first model proposed by Stephanov is directly related to QCD and allows to analyze the QCD phase diagram. In the second model suggested by the author all microscopic spectral correlation functions of complex Dirac operators can be calculated in the broken phase. We briefly compare those predictions to complex Dirac eigenvalues from quenched QCD lattice simulations.

PACS numbers: 12.38.Lg, 11.30.Rd, 05.40.--a