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Ferromagnetic Vacuum and Galactic Magnetic Fields

Non-abelian gauge theories may have a ferromagnet-like vacuum with a non-zero magnetic field, which also exists at finite temperature. We argue that the formation of the ferromagnet-like vacuum at GUT scales gives rise to a Maxwell magnetic field imprinted on the comoving plasma, and that it is energetically favourable to align the field in different correlation volumes. This results in a coherent magnetic field pertaining the whole universe, with a magnitude $B_{now}\simeq 10^{-14}\G$, which is of the correct size to serve as the seed field for the galactic dynamo.