A lattice Monte Carlo study of the hot electroweak phase transition

We study the finite temperature electroweak phase transition with lattice perturbation theory and Monte Carlo techniques. Dimensional reduction is used to approximate the full four-dimensional SU(2) + a fundamental doublet Higgs theory by an effective three-dimensional SU(2) + adjoint Higgs + fundamental Higgs theory with coefficients depending on temperature via screening masses and mass counterterms. Fermions contribute to the effective theory only via the $N_F$ and $m_{\rm top}$ dependence of the coefficients. For sufficiently small lattices ($N^3 < 30^3$ for $m_H$ = 35 GeV) the study of the one-loop lattice effective potential shows the existence of the {\em second} order phase transition even for the small Higgs masses. At the same time, a clear signal of a {\em first order} phase transition is seen on the lattice simulations with a transition temperature close to but less than the value determined from the perturbative calculations. This indicates that the dynamics of the first order electroweak phase transition depends strongly on non-perturbative effects and is not exclusively related to the so-called $\phi^3$ term in the effective potential.