Electroweak phase transition in a strong magnetic field
  Phase transitions induced by high temperatures and strong magnetic fields are investigated in the Standard model. The consistent effective potential including the one-loop and ring diagram contributions is calculated and investigated for the wide range of the fields, temperatures and Higgs boson mass $m_H$. All other particles - fermions and bosons - are taken into account with actual values of their masses. This effective potential is real at sufficiently high temperatures . It is shown that symmetry restoration is a first type phase transition for $m_H < 70 $ Gev . For heavier Higgs particles and the field strengths $H > 0.1 \cdot 10^{24} G $ the local electroweak minimum could not be realized at all. Hence, the upper limit on the Higgs mass as well as the limit on the field strengths in the phase transition epoch follow. 
V. Skalozub, M. Bordag