Deconfinement transitions in three-dimensional compact lattice Abelian Higgs models with multiple-charge scalar fields

We investigate the nature of the deconfinement transitions in three-dimensional lattice Abelian Higgs models, in which a complex scalar field of integer charge Q≥ 2 is minimally coupled with a compact $U(1)$ gauge field. Their phase diagram presents two phases separated by a transition line where static charges q, with $q<Q$, deconfine. We argue that these deconfinement transitions belong to the same universality class as transitions in generic three-dimensional ZQ gauge models. In particular, they are Ising-like for $Q=2$, of first order for $Q=3$, and belong to the three-dimensional gauge $XY$ universality class for Q≥ 4. This general scenario is supported by numerical finite-size scaling analyses of the energy cumulants for $Q=2$, $Q=4$, and $Q=6$.