A density wave in quark matter is discussed at finite temperature, which occurs along with the chiral condensation, and is described by a dual standing wave in scalar and pseudo-scalar condensates on the chiral circle. The mechanism is quite similar to that for the spin density wave suggested by Overhauser, and entirely reflects many-body effects. It is found within a mean-field approximation for NJL model that the chiral condensed phase with the density wave develops at a high-density region just outside the usual chiral-transition line in phase diagram. A magnetic property of the density wave is also elucidated.

We consider the thermodynamics of chiral models in the mean-field approximation and discuss the relevance of the (frequently omitted) fermion vacuum loop. Within the chiral quark-meson model and its Polyakov loop extended version, we show that the fermion vacuum fluctuations can change the order of the phase transition in the chiral limit and strongly influence physical observables. We compute the temperature-dependent effective potential and baryon number susceptibilities in these models, with and without the vacuum term, and explore the cutoff and the pion mass dependence of the susceptibilities. Finally, in the renormalized model the divergent vacuum contribution is removed using the dimensional regularization.Comment: 9 pages, 5 figure

We have studied a holographically dual description of superconductor in (2 + 1)-dimensions in the presence of applied magnetic field, and observed that there exists a critical value of magnetic field, below which a charged condensate can form via a second order phase transition.