Photon propagator, monopoles, and the thermal phase transition in three dimensional compact QED

We investigate the gauge boson propagator in the three dimensional compact Abelian gauge model in the Landau gauge at finite temperature. The presence of the monopole plasma in the confinement phase leads to the appearance of an anomalous dimension in the momentum dependence of the propagator. The anomalous dimension as well as an appropriate ratio of photon wave function renormalization constants with and without monopoles is observed to be an order parameter for the deconfinement phase transition. We discuss the relation between our results and the confining properties of the gluon propagator in non-Abelian gauge theories.