  Numerical simulations are performed to study the finite temperature phase
transition in the SU(2) Higgs model on the lattice. In the presently
investigated range of the Higgs boson mass, below 50 GeV, the phase transition
turns out to be of first order and its strength is rapidly decreasing with
increasing Higgs boson mass. In order to control the systematic errors, we also
perform studies of scaling violations and of finite volume effects.
