Chiral transition in a magnetic field and at finite baryon density

We consider the quark-meson model with two quark flavors in a constant external magnetic field B at finite-temperature T and finite baryon chemical potential mu(B). We calculate the full renormalized effective potential to one-loop order in perturbation theory. We study the system in the large-N-c limit, where we treat the bosonic modes at tree level. It is shown that the system exhibits dynamical chiral symmetry breaking, i.e. that an arbitrarily weak magnetic field breaks chiral symmetry dynamically, in agreement with earlier calculations using the Nambu-Jona-Lasinio model. We study the influence on the phase transition of the fermionic vacuum fluctuations. For strong magnetic fields, vertical bar qB vertical bar similar to 5m(pi)(2) and in the chiral limit, the transition is first order in the entire mu(B)-T plane if vacuum fluctuations are not included and second order if they are included. At the physical point, the transition is a crossover for mu(B) = 0 with and without vacuum fluctuations.