The stability of primordial magnetic fields produced by phase transitions

Primordial magnetic fields seem to be a generic relic of phase transitions in the early universe. We consider a primordial electromagnetic field formed as a result of a second-order phase transition, and show that it is stable to thermal fluctuations in the period immediately following. We also show how such a field arises in first order phase transitions. In both cases there is a transitive electric field produced during the transition.