Aspects of the phase diagram in (P)NJL-like models

We discuss three applications of NJL- and PNJL-like models to assess aspects of the QCD phase diagram: First, we study the effect of mesonic correlations on the pressure below and above the finite temperature phase transition within a nonlocal PNJL model beyond the mean-field approximation. Second, we reconstruct the phase boundary of an NJL model from a Taylor expansion of the chiral susceptibility about $\mu = 0$ and compare the result with the exact phase boundary. Finally, we demonstrate the realization of the "non-standard scenario" for the critical surface in a three-flavor PNJL model with a $\mu$-dependent determinant interaction.