  We show that the decaying magnetohydrodynamic turbulence leads to a more
rapid growth of the correlation length of a primordial magnetic field than that
caused by the expansion of the Universe. As an example, we consider the
magnetic fields created during the electroweak phase transition. The expansion
of the universe alone would yield a correlation length at the present epoch of
1 AU, whereas we find that the correlation length is likely of order 100 AU,
and cannot possibly be longer than $10^4$ AU for non-helical fields. If the
primordial field is strongly helical, the correlation length can be much
larger, but we show that even in this case it cannot exceed 100 pc. All these
estimates make it hard to believe that the observed galactic magnetic fields
can result from the amplification of seed fields generated at the electroweak
phase transition by the standard galactic dynamo.
