The infrared behaviour of the standard model at finite temperature is
determined by the confining phase of the SU(2)-Higgs model in three di
mensions. Due to the Landau singularity of the three-dimensional gauge
theory the perturbative treatment of the electroweak phase transition
breaks down for Higgs masses above a critical mass m(H)c. Based on a
renormalization group improved effective potential we find m(H)c appro
ximately 70 GeV. The scalar self-coupling has a Landau-type singularit
y also in the abelian U(1)-Higgs model, which leads to a breakdown of
perturbation theory in the symmetric phase.