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We compute the phase diagram of the quark-meson model at finite temperature,finite baryon chemical potential $\mu_B=3\mu$ and constant external magneticfield $B$, using the functional renormalization group. Our results show thatthe critical temperature increases as a function of $B$ at $\mu=0$, but forvalues $\mu$ larger than about 210-225 MeV, the opposite behavior is realized.As the magnetic field increases, the critical point $(T^*,\mu^*)$ moves fromlarge $\mu$, small $T$ towards small $\mu$, larger $T$ in the $\mu$--$T$ phasediagram.

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