Phase Structure and Gauge Boson Propagator in the radially active 3D   compact Abelian Higgs Model
  Unfreezing the radial degree of freedom, we study the three-dimensional Abelian Higgs model with compact gauge field and fundamentally charged matter. For small quartic Higgs self coupling and finite gauge coupling the model possesses a first order transition from the confined/symmetric phase to the deconfined/Higgs phase separated at some hopping parameter $\kappa_c$. Latent heat and surface tension are obtained in the first order regime. At larger quartic coupling the first order transition ceases to exist, and the behavior becomes similar to that known from the London limit. These observations are complemented by a study of the photon propagator in Landau gauge in the two different regimes. The problems afflicting the gauge fixing procedure are carefully investigated. We propose an improved gauge fixing algorithm which uses a finite subgroup in a preselection/preconditioning stage. The computational gain in the expensive confinement region is a speed-up factor around 10. The propagator in momentum space has a non-zero anomalous dimension in the confined phase whereas it vanishes in the Higgs phase. As far as the gauge boson propagator is concerned, we find that the radially active Higgs field provides qualitatively no new effect compared to the radially frozen Higgs field studied before. 
M. N. Chernodub, R. Feldmann, E.-M. Ilgenfritz and A. Schiller