The Non-Trivial Phase of ${\varphi }^4$-Theory in an External Magnetic Field and at Finite Temperature

The effective potential for the order parameter ${\varphi }^{†}\varphi$ is investigated in massless ${\varphi }^4$-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.