  By solving the gap equation in the quenched, ladder approximation for an
Abelian gauge model with Yukawa interaction in the presence of a constant
magnetic field, we show that the Yukawa interactions enhance the dynamical
generation of fermion mass. The theory is then studied at finite temperature,
where we prove that the critical magnetic field, required for the mass
generation to be important at temperatures comparable to the electroweak
critical temperature, can be substantially decreased due to the Yukawa
coupling.
