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 Z(Q) 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.