Ferromagnetism of two-flavor quark matter in chiral and/or color-superconducting phases at zero and finite temperatures

Abstract

We study the phase structure of the unpolarized and polarized two-flavor quark matters at zero and finite temperatures within the Nambu--Jona-Lasinio (NJL) model. We focus on the region, which includes the coexisting phase of quark-antiquark and diquark condensates. Generalizing the NJL model so as to describe the polarized quark matter, we compute the thermodynamic potential as a function of the quark chemical potential ($\mu$), the temperature ($T$), and the polarization parameter. The result heavily depends on the ratio $G_D / G_S$, where $G_S$ is the quark-antiquark coupling constant and $G_D$ is the diquark coupling constant. We find that, for small $G_D / G_S$, the "ferromagnetic" phase is energetically favored over the "paramagnetic" phase. On the other hand, for large $G_D / G_S$, there appears the window in the ($\mu, T$)-plane, in which the "paramagnetic" phase is favored.