  The static sectors of the electroweak Standard Model and QCD at finite
temperatures are described by 3d SU(N) Higgs models with scalars in the
fundamental and adjoint representation, respectively. I summarize the
non-perturbative physics of these theories like mass spectrum, string tension,
screening of the static potential and non-perturbative corrections to the Debye
mass, as obtained from recent lattice simulations. It is observed that in the
3d theory corresponding to the purely magnetic sector there is a larger
hierarchy between different quantities than between the electric ($\sim gT$)
and magnetic ($\sim g^2T$) sectors of finite T gauge theories, which are not
generally well separated.
