  We study the MSSM finite temperature electroweak phase transition with
lattice Monte Carlo simulations, for a large Higgs mass (m_H ~ 95 GeV) and
light stop masses (m_tR ~ 150...160 GeV). We employ a 3d effective field theory
approach, where the degrees of freedom appearing in the action are the SU(2)
and SU(3) gauge fields, the weakly interacting Higgs doublet, and the strongly
interacting stop triplet. We determine the phase diagram, the critical
temperatures, the scalar field expectation values, the latent heat, the
interface tension and the correlation lengths at the phase transition points.
Extrapolating the results to the infinite volume and continuum limits, we find
that the transition is stronger than indicated by 2-loop perturbation theory,
guaranteeing that the MSSM phase transition is strong enough for baryogenesis
in this regime. We also study the possibility of a two-stage phase transition,
in which the stop field gets an expectation value in an intermediate phase. We
find that a two-stage transition exists non-perturbatively, as well, but for
somewhat smaller stop masses than in perturbation theory. Finally, the latter
stage of the two-stage transition is found to be extremely strong, and thus it
might not be allowed in the cosmological environment.
