  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.
