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

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