  Starting from the Phi-derivable approximation scheme at leading-loop order,
the thermodynamical potential in a hot scalar theory, as well as in QED and
QCD, is expressed in terms of hard thermal loop propagators. This
nonperturbative approach is consistent with the leading-order perturbative
results, ultraviolet finite, and, for gauge theories, explicitly
gauge-invariant. For hot QCD it is argued that the resummed approximation is
applicable in the large-coupling regime, down to almost twice the transition
temperature.
