For realistic values of the Higgs boson mass the high temperature electroweak phase transition cannot be described perturbatively. The symmetric phase is governed by a strongly interacting SU(2) gauge theory. Typical masses of excitations and scales of condensates are set by the ``high temperature confinement scale'' ≈0.2T. For a Higgs boson mass around 100 GeV or above all aspects of the phase transition are highly nonperturbative. Near the critical temperature strong electroweak interactions are a dominant feature also in the phase with spontaneous symmetry breaking. Depending on the value of the Higgs boson mass the transition may be a first order phase transition or an analytical crossover.
@article{arxiv.hep-th/9408054,
title = {High Temperature Field Theory Beyond Perturbation Theory},
author = {Christof Wetterich},
journal= {arXiv preprint arXiv:hep-th/9408054},
year = {2008}
}