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Unfreezing the radial degree of freedom, we study the three-dimensionalAbelian Higgs model with compact gauge field and fundamentally charged matter.For small quartic Higgs self coupling and finite gauge coupling the modelpossesses a first order transition from the confined/symmetric phase to thedeconfined/Higgs phase separated at some hopping parameter $\kappa_c$. Latentheat and surface tension are obtained in the first order regime. At largerquartic coupling the first order transition ceases to exist, and the behaviorbecomes similar to that known from the London limit. These observations arecomplemented by a study of the photon propagator in Landau gauge in the twodifferent regimes. The problems afflicting the gauge fixing procedure arecarefully investigated. We propose an improved gauge fixing algorithm whichuses a finite subgroup in a preselection/preconditioning stage. Thecomputational gain in the expensive confinement region is a speed-up factoraround 10. The propagator in momentum space has a non-zero anomalous dimensionin the confined phase whereas it vanishes in the Higgs phase. As far as thegauge boson propagator is concerned, we find that the radially active Higgsfield provides qualitatively no new effect compared to the radially frozenHiggs field studied before.Comment: 15 pages, 10 figure

Phase structure and gauge boson propagator in the radially active 3D compact Abelian Higgs model