The electroweak phase transition in a magnetic field

We study the finite temperature electroweak phase transition in an external hypercharge U(1) magnetic field H-Y, using lattice Monte Carlo simulations. For sufficiently small fields, H-Y/T-2 less than or similar to 0.3, the magnetic field makes the first-order transition stronger, but it still turns into a crossover for Higgs masses m(H) less than or similar to 80 GeV. For larger fields, we observe a mixed phase analogous to a type I superconductor, where a single macroscopic tube of the symmetric phase, parallel to H-Y, penetrates through the broken phase, For the magnetic fields and Higgs masses studied, we did not see indications of the expected Ambjorn-Olesen phase, which should be similar to a type II superconductor. (C) 1999 Elsevier Science B.V.