  In earlier work, we set up an effective potential approach at zero
temperature for the Gribov-Zwanziger model that takes into account not only the
restriction to the first Gribov region as a way to deal with the gauge fixing
ambiguity, but also the effect of dynamical dimension-two vacuum condensates.
Here, we investigate the model at finite temperature in presence of a
background gauge field that allows access to the Polyakov loop expectation
value and the Yang-Mills (de)confinement phase structure. This necessitates
paying attention to BRST and background gauge invariance of the whole
construct. We employ two such methods as proposed elsewhere in literature: one
based on using an appropriate dressed, BRST invariant, gluon field by the
authors and one based on a Wilson-loop dressed Gribov-Zwanziger auxiliary field
sector by Kroff and Reinosa. The latter approach outperforms the former, in
estimating the critical temperature for N=2, 3 as well as correctly predicting
the order of the transition for both cases.
