  We study the critical behavior of three-dimensional (3D) lattice
Abelian-Higgs (AH) gauge models with noncompact gauge variables and
multicomponent complex scalar fields, along the transition line between the
Coulomb and Higgs phases. Previous works that focused on gauge-invariant
correlations provided evidence that, for a sufficiently large number of scalar
components, these transitions are continuous and associated with the stable
charged fixed point of the renormalization-group flow of the 3D AH field theory
(scalar electrodynamics), in which charged scalar matter is minimally coupled
with an electromagnetic field. Here we extend these studies by considering
gauge-dependent correlations of the gauge and matter fields, in the presence of
two different gauge fixings, the Lorenz and the axial gauge fixing. Our results
for N=25 are definitely consistent with the predictions of the AH field theory
and therefore provide additional evidence for the characterization of the 3D AH
transitions along the Coulomb-Higgs line as charged transitions in the AH
field-theory universality class. Moreover, our results give additional insights
on the role of the gauge fixing at charged transitions. In particular, we show
that scalar correlations are critical only if a hard Lorenz gauge fixing is
imposed.
