  In this letter, we study the productions of magnetic fields and gravitational
waves from the first-order phase transition. We perform numerical simulations
of the evolutions of Higgs fields, and gauge fields after supplementing the
bubble nucleations and obtain the power-law spectra of the gravitational wave
and the magnetic field strength. Our study suggests that the observation of
cosmic magnetic field strength and the gravitational waves can be complementary
to probe features of first-order phase transitions occurring in the early
Universe.
