  We propose the study of the phase transition in the scalar electroweak theory
at finite temperature by a two - step method. It combines i) dimensional
reduction to a 3-dimensional {\it lattice\/} theory via perturbative blockspin
transformation, and ii) either further real space renormalization group
transformations, or solution of gap equations, for the 3d lattice theory. A gap
equation can be obtained by using the Peierls inequality to find the best
quadratic approximation to the 3d action. % This method avoids the lack of self
consistency of the usual treatments which do not separate infrared and
UV-problems by introduction of a lattice cutoff. The effective 3d lattice
action could also be used in computer simulations.
