Inhomogeneous phases in the Nambu-Jona-Lasinio and quark-meson model

We discuss inhomogeneous ground states of the Nambu-Jona-Lasinio and quark-meson model within mean-field approximation and their possible existence in the respective phase diagrams. For this purpose we focus on lower-dimensional modulations and point out that known solutions in the 2 + 1 and 1 + 1 dimensional ( chiral) Gross-Neveu model can be lifted to the to the 3 + 1 dimensional Nambu-Jona-Lasinio model. This is worked out in detail for one-dimensional modulations and numerical results for the phase diagrams are presented. Focus is put on the critical point and on vanishing temperatures. As an interesting result the first order transition line in the phase diagram of homogeneous phases gets replaced by an inhomogeneous phase which is bordered by two second order transition lines.