The QCD phase diagram in the presence of an external magnetic field: the role of the inverse magnetic catalysis

The effect of an external magnetic field in QCD phase diagram, namely, in the the location of the critical end point (CEP) is investigated. Using the 2+1 flavor Nambu--Jona-Lasinio model with Polyakov loop, it is shown that when an external magnetic field is applied its effect on the CEP depends on the strength of the coupling. If the coupling depends on the magnetic field, allowing for inverse magnetic catalysis, the CEP moves to lower chemical potentials eventually disappearing, and the chiral restoration phase transition is always of first order.