Static mass scales in hot gauge theories

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.