NUMERICAL APPROACH TO THE ONSET OF THE ELECTROWEAK PHASE-TRANSITION

We investigate whether the universe was homogeneously in the false vac uum state at the critical temperature of a weakly first-order phase tr ansition such as the electroweak phase transition in terms of a series of numerical simulations of a phenomenological Langevin equation, who se noise term is derived from the effective action but the dissipative term is set so that the fluctuation-dissipation relation is met. The correlation function of the noise terms given by a nonequilibrium fiel d theory has a distinct feature if it originates from interactions wit h a boson or with a fermion. The spatial correlation function of noise s from a massless boson damps with a power law, while the fermionic no ises always damp exponentially above the inverse-temperature scale. In the simulation with the one-loop effective potential of the Higgs fie ld, the latter turns out to be more effective to disturb the homogeneo us field configuration. Since noises of both types are present in the electroweak phase transition, our results suggest that the conventiona l picture of a phase transition, namely, nucleation of critical bubble s in a homogeneous background, does not apply or the one-loop approxim ation breaks down in the standard model. [S0556-2821(97)01220-4].