  In this work we study the dynamical generation of a fermion mass induced by a
constant and uniform external magnetic field in an Abelian gauge model with a
Yukawa term. We show that the Yukawa coupling not only enhances the dynamical
generation of the mass, but it substantially decreases the magnetic field
required for the mass to be generated at temperatures comparable to the
electroweak critical temperature. These results indicate that if large enough
primordial magnetic fields were present during the early universe evolution,
the field-induced generation of fermion masses, which in turn corresponds to
the generation of fermion bound states, may play an important role in the
electroweak phase transition.
