  We study the confinement-deconfinement phase transition of pure Yang-Mills
theories at finite temperature using a simple massive extension of standard
background field methods. We generalize our recent next-to-leading-order
perturbative calculation of the Polyakov loop and of the related background
field effective potential for the SU(2) theory to any compact and connex Lie
group with a simple Lie algebra. We discuss in detail the SU(3) theory, where
the two-loop corrections yield improved values for the first-order transition
temperature as compared to the one-loop result. We also show that certain
one-loop artifacts of thermodynamical observables disappear at two-loop order,
as was already the case for the SU(2) theory. In particular, the entropy and
the pressure are positive for all temperatures. Finally, we discuss the groups
SU(4) and Sp(2) which shed interesting light, respectively, on the relation
between the (de)confinement of static matter sources in the various
representations of the gauge group and on the use of the background field
itself as an order parameter for confinement. In both cases, we obtain
first-order transitions, in agreement with lattice simulations and other
continuum approaches.
