Scalar gauge-Higgs models with discrete Abelian symmetry groups

We investigate the phase diagram and the nature of the phase transitions of three-dimensional lattice gaugeHiggs models obtained by gauging the ZN subgroup of the global Zq invariance group of the Zq clock model (N is a submultiple of q). The phase diagram is generally characterized by the presence of three different phases, separated by three distinct transition lines. We investigate the critical behavior along the two transition lines characterized by the ordering of the scalar field. Along the transition line separating the disordered-confined phase from the ordered-deconfined phase, standard arguments within the Landau-Ginzburg-Wilson framework predict that the behavior is the same as in a generic ferromagnetic model with Zp global symmetry, p being the ratio q/N. Thus, continuous transitions belong to the Ising and to the O(2) universality class for p = 2 and p 4, respectively, while for p = 3 only first-order transitions are possible. The results of Monte Carlo simulations confirm these predictions. There is also a second transition line, which separates two phases in which gauge fields are essentially ordered. Along this line we observe the same critical behavior as in the Zq clock model, as it occurs in the absence of gauge fields.