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