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the standard model of electroweak interactions predicts the existence of a phase transition inbetween a low temperature symmetry broken and a high temperature symmetric phase @xcite . its thermodynamic properties lead to cosmological consequences . one might hope that the baryon asymmetry can be generated at the electroweak phase transition , if the transition is of strong first order . for values of the zero temperature higgs - mass @xmath3 gev the phase transition is of first order @xcite . as the higgs - mass is increased further , the thermodynamic singularity at the electroweak phase transition weakens . it is even possible , that for large values of the higgs - mass the phase transition loses its nonanalytical structure and is described by a crossover @xcite . in the strict sense the electroweak phase transition would then cease to exist . the exact determination of the critical higgs - mass value @xmath4 , at which the first order electroweak phase transition changes from first order to a crossover is important in view of its implications for the standard model . another aspect of the electroweak theory is the non - vanishing magnetic screening mass . it controls the infrared behavior of the theory at high temperatures and influences the nature of the phase transition itself . this work is a continuation of earlier studies and for details on the formulation of the theory we refer to @xcite . here we recall the simulated @xmath5 action functional : @xmath6    the relationship of the dimensionless lattice couplings @xmath7 to the couplings of the @xmath8 @xmath9 gauge - higgs system can be found in @xcite . our simulation is performed at @xmath10 and at @xmath11 values @xmath12 and @xmath13 . the hopping parameter is varied across the phase transition . these @xmath14-values correspond to higgs - mass values of @xmath15 and @xmath16 gev , if the 1-loop parameter mapping of @xcite is used . for possible correction terms inducing small corrections to the here cited higgs - mass values we refer to a forthcoming publication . to illustrate the critical behavior as a function of @xmath14 , or the higgs - mass , we display in figure [ cv_max ] the maxima of the @xmath17-susceptibility , which is given by @xmath18    3.0 in -0.5 in cv_max cv_max.eps maxima of the @xmath17-susceptibility . we investigate lattice sizes ranging from @xmath19 up to @xmath20 . the labeling of the data in figure [ cv_max ] corresponds to the one used in figure [ l_im ] . the data at @xmath21 are consistent with a first order transition , the dotted line with slope @xmath22 in the figure . at @xmath23 and @xmath13 a crossover is observed , while at @xmath24 the behavior is almost critical , the solid scaling curve in figure [ chi ] . the determination of the critical higgs - mass value relies on the analysis of fisher or lee - yang zeroes @xcite in the crossover - region of the theory . the partition function @xmath25 is analytically continued into the complex plane as a function of the complex hopping parameter @xmath26 . denoting with @xmath27 the lowest zero of @xmath25 , i.e. the zero in @xmath26 with smallest length , we expect in the vicinity of the critical end - point the scaling law @xmath28 such a scaling behavior can also be observed for lee - yang zeroes in the high temperature phase of the ising model . our strategy to localize the end - point then is to determine the value of @xmath14 , at which the regular contribution @xmath29 to the scaling law vanishes : @xmath30 . in figure [ l_im ] we display @xmath31 vs. @xmath32 . the solid curves in figure [ l_im ] correspond to fits with the scaling law . 3.0 in -0.5 in l_im l_im.eps imaginary parts of the lowest zeroes of the partition function .    in figure [ fitconst ] the constant @xmath33 is displayed as function of @xmath14 . the data are consistent with a linear dependence on @xmath14 and the fit results into @xmath34 , corresponding to a critical higgs - mass value of approximately @xmath35 gev . 3.0 in -0.5 in fitconst fitconst.eps the determination of @xmath36 . the w - boson mass is determined from the w - boson propagator in landau - gauge , @xmath37 . for a detailed discussion of the implementation of the landau - gauge on a lattice see @xcite and references therein . we investigate the w - boson propagator at @xmath24 , which is very close to the critical higgs - mass . simulations have been performed on a @xmath38 lattice . the propagators have been analyzed in the same way as discussed in @xcite . our results are shown in figure [ mass_w ] . 3.0 in -0.6 in mass_w mass_w.eps w - boson screening masses , calculated on a @xmath38 lattice at @xmath24 . the full curve describes the fit to the data . the dashed curve represents the result obtained from gap equations .    in the high temperature phase the w - boson propagator stays constant . a fit to the data for @xmath39 , the full triangles in the figure , yields @xmath40 . it is worthwhile to note , that in pure su(2 ) gauge theory the magnetic screening mass has a value @xmath41 , the horizontal full and dotted lines in figure [ mass_w ] . in the symmetry broken phase the mass increases rapidly . in this region the data are very well described by the ansatz @xmath42 the fit to the full circles in the figure results into a value for the exponent @xmath43 of @xmath44 . we are now able to compare our results with predictions based on gap equations @xcite . using similar parameters in the gap equations as in our study we observe a qualitative agreement , the dashed curve in the figure . we have exploited the scaling behavior of partition function zeroes in the vicinity of the critical end - point in order to determine the critical higgs - mass @xmath4 . the electroweak phase transition looses its first order character at a higgs - mass value of about @xmath35 gev . close to the critical higgs - mass we have measured the w - boson propagator in landau gauge . w - boson screening masses remain constant in the high temperature symmetric phase and increase in the low temperature higgs phase . the agreement of these data with predictions based on gap equations is of qualitative nature .
we study the effective 3-d su(2 ) gauge - higgs model at finite temperature for higgs - masses in the range from @xmath0 gev up to @xmath1 gev . 
 the first order electroweak phase transition weakens with increasing higgs - mass and terminates at a critical end - point . for higgs - mass values larger than about @xmath2 gev 
 the thermodynamic signature of the transition is described by a crossover . 
 close to this higgs - mass value we investigate the vector boson propagator in landau gauge . 
 the calculated w - boson screening masses are compared with predictions based on gap equations . 
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