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, $|qB|\sim 5m_{\pi }^2$ and in the chiral limit, the transition is first order in the entire ${\mu }_B\mathrm{\text{-}}T$ 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. DOI: http://dx.doi.org/10.1103/PhysRevD.85.065026 © 2012 American Physical Society

We investigate the chiral phase transition in the quark‐meson effective model using optimised perturbation theory to one loop. Certain terms in the free energy are frequently omitted in calculations, on the assumption that their contribution is negligible. We show that this is not necessarily the case, and that the order of the phase transition, as well as the critical temperature, depends heavily on which contributions are included.