  We consider the classical vacua of the Weinberg-Salam (WS) model of
electroweak forces. These are no-particle, static solutions to the WS equations
minimizing the WS energy locally.
  We study the WS vacuum solutions exhibiting a non-vanishing average magnetic
field of strength $b$, and prove that (i) there is a magnetic field threshold
$b_*$ such that for $b < b_*$, the vacua are translationally invariant (and the
magnetic field is constant), while for $b > b_*$ they are not, (ii) for $b >
b_*$, there are non-translationally invariant solutions with lower energy per
unit volume and with the discrete translational symmetry of a 2D lattice in the
plan transversal to $b$, and (iii) the lattice minimizing the energy per unit
volume approaches the hexagonal one as the magnetic field strength approaches
the threshold $b_*$.
  In the absence of particles, the Weinberg-Salam model reduces to the
Yang-Mills-Higgs (YMH) equations for the gauge group $U(2)$. Thus our results
can be rephrased as the corresponding statements about the $U(2)$-YMH
equations.
