Magnetic field and gravitational waves from the first-order Phase
  Transition
  We perform the three dimensional lattice simulation of the magnetic field and
gravitational wave productions from bubble collisions during the first-order
electroweak phase transition. Except that of the gravitational wave, the
power-law spectrum of the magnetic field strength is numerically calculated for
the first time, which is of a broken power-law spectrum: $B_{\xi}\propto
f^{0.91}$ for low frequency region of $f<f_\star$ and $B_{\xi}\propto
f^{-1.65}$ for high frequency region of $f>f_\star$ in the thin-wall limit,
with the peak frequency being $f_\star\sim 5$ Hz at the phase transition
temperature 100 GeV. When the hydrodynamics is taken into account, the
generated magnetic field strength can reach $B_\xi\sim 10^{-7}$G at a
correlation length $\xi\sim 10^{-7}$pc, which may seed the large scale magnetic
fields. Our study shows that the measurements of cosmic magnetic field strength
and gravitational waves are complementary to probe new physics admitting
electroweak phase transition.
