Area law for spatial Wilson loops in high-temperature lattice gauge theories

It has been pointed out that the behavior of space-like Wilson loops in non-zero temperature lattice gauge theories cannot be considered as a confinement criterion. In particular they may show area law behavior in the deconfinement phase. We rigorously establish this for sufficiently high temperatures by means of a cluster expansion. For abelian theories correlation inequalities imply a stronger result: space-like Wilson loops in the (d+1)-dimensional theory (at coupling g2 and temperature T) show area law whenever the corresponding d-dimensional 0 temperature theory (with coupling Tg2) is confining. Our results remain valid in the tau-continuum limit. (orig.)