Ginzburg-Landau approach to inhomogeneous chiral phases of QCD

We study the inhomogeneous chiral condensates in the proximity of the chiral tricritical point (TCP) of two-flavor QCD. Deriving the Ginzburg-Landau (GL) functional up to the eighth order in the order parameter and its spatial derivative, we explore off the TCP and find that critical curves are bent by non-linear effects. In the newly extend GL coupling space, we find the TCP being realized as a multicritical point where five independent critical lines meet up. We also present general analyses for the energies associated with several higher dimensional crystal structures.