Gluon propagator close to criticality.

There are good reasons that the deconfinement phase transition of pure Yang-Mills theory at finite temperature should also be reflected in the behavior of gauge-fixed gluonic correlation functions. Understanding this in detail would provide another important example of how physical information can be extracted from gauge-dependent correlations, which is not always obvious. Therefore, herein we study the behavior of the Landau-gauge gluon propagator of pure SU(2) across the phase transition in 2 + 1 and 3 + 1 dimensions in order to assess to what extend the corresponding critical behavior is reflected in these correlations. We discuss why it should emerge from a continuum perspective and test our expectations in lattice simulations. A comparison with SU(3) furthermore reveals quite clear indications for a sensitivity of the gluon propagator to the order of the transition. [ABSTRACT FROM AUTHOR]