Analytical studies for the critical line and critical endpoint of the electroweak phase transition

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.