  The infrared dynamics in the (3+1)-dimensional supersymmetric and
non-supersymmetric Nambu-Jona-Lasinio model in a constant magnetic field is
studied. While at strong coupling the dynamics in these two models is
essentially different, it is shown that the models become equivalent at weak
coupling. In particular, at weak coupling, as the strength of the magnetic
field goes to infinity, both the supersymmetric and non-supersymmetric
Nambu-Jona-Lasinio models are reduced to a continuum set of independent
(1+1)-dimensional Gross-Neveu models, labeled by the coordinates in the plane
perpendicular to the magnetic field. The relevance of these results for
cosmological models based on supersymmetric dynamics is pointed out.
