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 - 225MeV, the opposite behavior is realized. As the magnetic field increases, the critical point (T*, mu*) moves from large mu, small T towards small mu, larger T in the mu-T phase diagram.