Ferromagnetism in quark matter

Abstract

We investigate the magnetic property of the cold quark matter employing the magnetic moment ${\vec{\mu }}^{\prime }$ as the order parameter. Through analysis of the effective potential $V({\vec{\mu }}^{{}^{\prime }2})$, we find that, at relatively high densities $\rho >{\rho }_c$, the quark matter is in the normal phase. At $\rho ={\rho }_c$, the magnetic phase transition takes place and, in the low-density region $\rho <{\rho }_c$, the quark matter is in the ferromagnetic phase. For up, down and strange quarks, ${\rho }_c=1.62{\rho }_0$, $1.47{\rho }_0$ and $2.20{\rho }_0$ (${\rho }_0$ the nuclear density), respectively. We also find that the leptons ($e$ and $\mu$) inside the quark matter are in the normal phase.

22 pages, 13 figures