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.

We present detailed Monte Carlo results for the two-dimensional melting transition of various systems up to N = 65536 hard disks. The simulations are performed in the N V T ensemble, using a new updating scheme. In the isotropic phase the bond orientational correlation length ξ 6 and the susceptibility χ 6 are measured and compared with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory. From the scaling relation of ξ 6 and χ 6 we calculate the critical exponent η 6 . In the phase transition region we use finite-size scaling methods to locate the disclination binding transition point and compare the results with the values obtained from the behaviour in the isotropic phase. Additionally, we measure the topological defect density, the pressure and the distribution of the second moment of the local bond orientational order parameter. All results are in good agreement with the KTHNY theory, while a first-order phase transition with small correlation length and a one-stage continuous transition can be ruled out.

Comprehensive Monte Carlo simulations of the short-time dynamic behaviour are reported for the three-dimensional Ising model at criticality. Besides the exponent θ of the critical initial increase and the dynamic exponent z, the static critical exponents ν and β as well as the critical temperature are determined from the power-law scaling behaviour of observables at the beginning of the time evolution. States of very high temperature as well as of zero temperature are used as initial states for the simulations. PACS: 64.60.Cn, 75.10.Hk, 64.60.Ht, 75.40.Mg * Work supported in part by the Deutsche Forschungsgemeinschaft; DFG Schu 95/9-1 and SFB 418 1 For a recent review see Ref. [2].

The finite temperature phase transition in the SU(2) Higgs model at a Higgs boson mass M H ≃ 34 GeV is studied in numerical simulations on four-dimensional lattices with time-like extensions up to L t = 5. The effects of the finite volume and finite lattice spacing on masses and couplings are studied in detail. The errors due to uncertainties in the critical hopping parameter are estimated. The thermodynamics of the electroweak plasma near the phase transition is investigated by determining the relation between energy density and pressure.

Numerical simulations are performed to study the finite temperature phase transition in the SU(2) Higgs model on the lattice. The strength of the first order phase transition is investigated by determining the latent heat and the interface tension on L t = 2 lattices. The values of the Higgs boson mass presently chosen are below 50 GeV. Our results are in qualitative agreement with two-loop resummed perturbation theory.