  We investigate under which conditions the three-dimensional (3D)
multicomponent Abelian-Higgs (AH) field theory (scalar electrodynamics) is the
continuum limit of statistical lattice gauge models, i.e., when it
characterizes the universal behavior at critical transitions occurring in these
models. We perform Monte Carlo simulations of the lattice AH model with compact
gauge fields and $N$-component scalar fields with charge $q\ge 2$ for $N=15$
and 25. Finite-size scaling analyses of the Monte Carlo data show that the
transitions along the line separating the confined and deconfined phases are
continuous and that they belong to the same universality class for any $q\ge
2$. Moreover, they are in the same universality class as the transitions in the
lattice AH model with noncompact gauge fields along the Coulomb-to-Higgs
transition line. We finally argue that these critical behaviors are described
by the stable charged fixed point of the renormalization-group flow of the 3D
AH field theory.
