Quark matter under strong magnetic field in chiral models

The chiral model is used to describe quark matter under strong magnetic fields and compared to other models, the MIT bag model and the two flavors Nambu-Jona-Lasinio model. The effect of vacuum corrections due to the magnetic field is discussed. It is shown that if the magnetic field vacuum corrections are not taken into account explicitly the parameters of the models should be fitted to low density meson properties in the presence of the magnetic field.