  We outline two approaches for studying the electroweak phase transition in
the framework of the four-dimensional SU(2) Higgs model on a lattice. The first
one is based on a combination of variational estimates for the free energy and
a solution of the resulting gap equations by means of dynamical linked cluster
expansions. In the second approach we first indicate the derivation of an
effective scalar field theory upon integration over the gauge fields. The phase
structure of the resulting scalar theory is then investigated by means of
generalized linked cluster expansions. We present results for the critical line
and the critical endpoint.
