Vortex phases in condensed matter and cosmology

Placing a high-Tc superconductor in an increasing external magnetic field, the flux first penetrates the sample through an Abrikosov vortex lattice, and then a first order transition is observed by which the system goes to the normal phase. We discuss the cosmological motivation for considering the electroweak phase transition in the presence of an external magnetic field, the analogies this system might have with the superconductor behaviour described above, and in particular whether at large physical Higgs masses, corresponding to the high-Tc regime, an analogue of the vortex phase and an associated first order phase transition could be generated.