  Non-perturbative lattice simulations have shown that there is no electroweak
phase transition in the Standard Model for the allowed Higgs masses, m_H \gsim
75 GeV. In the Minimal Supersymmetric Standard Model, in contrast, it has been
proposed that the transition should exist and even be strong enough for
baryogenesis up to m_H ~ 105 GeV, provided that the lightest stop mass is in
the range 100...160 GeV. However, this prediction is based on perturbation
theory, and suffers from a noticeable gauge parameter and renormalization scale
dependence. We have performed large-scale lattice Monte Carlo simulations of
the MSSM electroweak phase transition. Extrapolating the results to the
infinite volume and continuum limits, we find that the transition is in fact
stronger than indicated by 2-loop perturbation theory. This guarantees that the
perturbative Higgs mass bound m_H ~ 105 GeV is a conservative one, allows
slightly larger stop masses (up to ~ 165 GeV), and provides a strong motivation
for further studies of MSSM electroweak baryogenesis.
