  The effective potential for the order parameter $\phi ^{\dagger } \phi$ is
investigated in massless $\phi ^{4}$-theory in the presence of magnetic fields
at finite temperature. It is found that the first order nature of the phase
transition from the non-trivial to the perturbative ground state at a critical
temperature is unchanged by the presence of magnetic fields, though they do
increase the critical temperature and weaken the barrier separating the
perturbative from the non-trivial phase. The results might be relevant for the
electro-weak phase transition as well as for inflationary models of the early
universe.
