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We investigate the phase diagram and the nature of the phase transitions ofthree-dimensional lattice gauge-Higgs models obtained by gauging the Z_Nsubgroup of the global Z_q invariance group of the Z_q clock model (N is asubmultiple of q). The phase diagram is generally characterized by the presenceof three different phases, separated by three distinct transition lines. Weinvestigate the critical behavior along the two transition lines characterizedby the ordering of the scalar field. Along the transition line separating thedisordered-confined phase from the ordered-deconfined phase, standard argumentswithin the Landau-Ginzburg-Wilson framework predict that the behavior is thesame as in a generic ferromagnetic model with Z_p global symmetry, p being theratio q/N. Thus, continuous transitions belong to the Ising and to the O(2)universality class for p=2 and p>3, respectively, while for p=3 onlyfirst-order transitions are possible. The results of Monte Carlo simulationsconfirm these predictions. There is also a second transition line, whichseparates two phases in which gauge fields are essentially ordered. Along thisline we observe the same critical behavior as in the Z_q clock model, as itoccurs in the absence of gauge fields.

Scalar gauge-Higgs models with discrete Abelian symmetry groups