  The effect of an applied magnetic field in the crossover from Bose-Einstein
condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) pairing regimes is
investigated. We use a model of relativistic fermions and bosons inspired by
those previously used in the context of cold fermionic atoms and in the
magnetic-color-flavor-locking phase of color superconductivity. It turns out
that as with cold atom systems, an applied magnetic field can also tune the
BCS-BEC crossover in the relativistic case. We find that no matter what the
initial state is at B=0, for large enough magnetic fields the system always
settles into a pure BCS regime. In contrast to the atomic case, the magnetic
field tuning of the crossover in the relativistic system is not connected to a
Feshbach resonance, but to the relative numbers of Landau levels with either
BEC or BCS type of dispersion relations that are occupied at each magnetic
field strength.
