  The QCD phase diagram in the temperature versus quark chemical potential
plane is studied in the presence of a magnetic field, using the linear sigma
model coupled to quarks. It is shown that the decrease of the couplings with
increasing field strength obtained in this model leads to the critical
temperature for the phase transition to decrease with increasing field
intensity (inverse magnetic catalysis). This happens provided that plasma
screening is properly accounted for. It is also found that with increasing
field strength the location of the critical end point (CEP) in the phase
diagram moves toward lower values of the critical quark chemical potential and
larger values of the critical temperature. In addition, the CEP approaches the
temperature axis for large values of the magnetic field. We argue that a
similar behavior is to be expected in QCD, since the physical impact of the
magnetic field, regardless of strength, is to produce a spatial dimension
reduction, whereby virtual quark-antiquark pairs are closer on average and
thus, the strength of their interaction decreases due to asymptotic freedom.
