  It is assumed that long range coherent magnetic fields in the universe were
spontaneously generated at high temperature due to vacuum polarization of
non-Abelian gauge fields, and resulted in the present intergalaxy magnetic
field. The zero value of the screening mass for fields of this type was
discovered recently. Here, a procedure to estimate the field strengths at
different temperatures is developed and the lower bound on the magnetic field
strength $B \sim 10^{14} G$, at the electroweak phase transition temperature,
is derived. As a particular case, the standard model is considered. Some model
dependent peculiarities of the phenomena under investigation are briefly
discussed.
