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 m
agnetic 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 superconduct
or, where a single macroscopic tube of the symmetric phase, parallel to H-Y
, penetrates through the broken phase, For the magnetic fields and Higgs ma
sses studied, we did not see indications of the expected Ambjorn-Olesen pha
se, which should be similar to a type II superconductor. (C) 1999 Elsevier
Science B.V.