Az elektrogyenge f\'azis\'atmenet (The electroweak phase transition)
  The electroweak phase transition provides the most attractive framework to account for the baryon asymmetry of the universe. Comparing results of perturbative and nonperturbative studies is not straightforward, however, due to the different coupling constant definitions. The perturbative one stems from the $\bar{\mathrm{MS}}$ subtraction scheme, while the nonperturbative one uses the static quark potential. The momentum-space perturbative static potential is calculated in the SU(2)--Higgs model, and is Fourier transformed into coordinate space. Based on the connection between the coupling constants, two-loop perturbative and 4-dimensional lattice simulation results are contrasted. The thermodynamical parameters of the phase transition indicate that perturbative results are reliable only for low Higgs masses, far from the endpoint. The value of the endpoint can be refined to $72.1\pm1.4$ GeV. The Higgs mass range for which dimensional reduction yields reliable results is identified. As an extension of the standard model, the MSSM is also studied. Some useful trends are indicated by a simple one-loop perturbative approach: baryogenesis requirements are more easily met if the stop is lighter thanthe top; colour-breaking phase transition may be possible, etc. In order to perform 4D nonperturbative studies the supercomputer PMS was built at E\"otv\"os University. The results and the techniques of the simulations of the bosonic sector of the MSSM performed on PMS are presented. A phase diagram is given, the bubble wall is studied. The cosmologically relevant part of the parameter space is analysed. The results show that baryogenesis is possible within the MSSM if $m_h\leq 103\pm 4$ GeV. 
A. Pir\'oth (Dept. for Theoretical Physics, E\"otv\"os University,   Budapest)