  Non-perturbative effects of constant magnetic fields in a Higgs-Yukawa gauge
model are studied using the extremum equations of the effective action for
composite operators. It is found that the magnetic field induces a Higgs
condensate, a fermion-antifermion condensate, and a fermion dynamical mass,
hence breaking the discrete chiral symmetry of the theory. The results imply
that for a non-simple group extension of the present model, the external
magnetic field would either induce or reinforce gauge symmetry breaking.
Possible cosmological applications of these results in the electroweak phase
transition are suggested.
