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We study the critical behavior of three-dimensional (3D) latticeAbelian-Higgs (AH) gauge models with noncompact gauge variables andmulticomponent complex scalar fields, along the transition line between theCoulomb and Higgs phases. Previous works that focused on gauge-invariantcorrelations provided evidence that, for a sufficiently large number of scalarcomponents, these transitions are continuous and associated with the stablecharged fixed point of the renormalization-group flow of the 3D AH field theory(scalar electrodynamics), in which charged scalar matter is minimally coupledwith an electromagnetic field. Here we extend these studies by consideringgauge-dependent correlations of the gauge and matter fields, in the presence oftwo different gauge fixings, the Lorenz and the axial gauge fixing. Our resultsfor N=25 are definitely consistent with the predictions of the AH field theoryand therefore provide additional evidence for the characterization of the 3D AHtransitions along the Coulomb-Higgs line as charged transitions in the AHfield-theory universality class. Moreover, our results give additional insightson the role of the gauge fixing at charged transitions. In particular, we showthat scalar correlations are critical only if a hard Lorenz gauge fixing isimposed.

The Coulomb-Higgs phase transition of three-dimensional lattice Abelian-Higgs gauge models with noncompact gauge variables and gauge fixing