The chiral transition in a magnetic background: Finite density effects and the functional renormalization group

We compute the phase diagram of the quark-meson model at finite temperature, finite baryon chemical potential ${\mu }_B=3\mu$ and constant external magnetic field $B$, using the functional renormalization group. Our results show that the critical temperature increases as a function of $B$ at $\mu =0$, but for values $\mu$ larger than about 210-225 MeV, the opposite behavior is realized. As the magnetic field increases, the critical point $(T^{\ast },{\mu }^{\ast })$ moves from large $\mu$, small $T$ towards small $\mu$, larger $T$ in the $\mu$–$T$ phase diagram.