  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 < 0.3, the magnetic field makes the first
order transition stronger, but it still turns into a crossover for Higgs masses
m_H ~ 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.
