  The continuum 3d SU(2)$\times$U(1)+Higgs theory is an effective theory for a
large class of 4d high-temperature gauge theories, including the minimal
standard model and some of its supersymmetric extensions. We study the effects
of the U(1) subgroup using lattice Monte Carlo techniques. When $g'^2/g^2$ is
increased from the zero corresponding to pure SU(2)+Higgs theory, the phase
transition gets stronger. However, the increase in the strength is close to
what is expected perturbatively, and the qualitative features of the phase
diagram remain the same as for $g'^2=0$. In particular, the first order
transition still disappears for $m_H>m_{H,c}$. We measure the photon mass and
mixing angle, and find that the mass vanishes in both phases within the
statistical errors.
