The Quark-meson model in a magnetic field

In this thesis we study the chiral phase transition of two-flavor QCD, through the use of the quark-meson model. The effect of a magnetic field on the transition is studied, at finite temperature and baryon chemical potential. The first few sections of the text are devoted to a short introduction to QCD and its thermodynamics, followed by derivations of the free energy of the free complex scalar field and the free fermion field. The quark-meson model is then introduced, and its effective potential computed to one-loop order. The parameters of the model are matched to physical observables taking loop corrections into account. Finally, numerical results are presented. The results are in line with predictions from other effective models, however, they diverge from current lattice results on the topic of magnetic catalysis