The electroweak phase transition at m$_{H}$ $\appprox$ m$_{W}$

We study the finite temperature electroweak transition with non-perturbative lattice Monte Carlo simulations. We find that it is of first order, at least for Higgs masses up to 80 GeV. The critical temperature of the phase transition is found to be smaller than that determined by a 2-loop renormalization group improved effective potential. The jump of the order parameter at the critical temperature is considerably larger than the perturbative value. By comparing lattice data and perturbation theory, we demonstrate that the latter, for the computation of the vacuum expectation value of the Higgs field v(T) in the broken phase at given temperature, converges quite well, provided v(T)/T>1. An upper bound on the Higgs mass necessary for electroweak baryogenesis in the light of the lattice data is briefly discussed.