Multicomponent gauge-Higgs models with discrete Abelian gauge groups

We consider a variant of the charge -Q compact Abelian-Higgs model, in which an N-f-dimensional complex vector is coupled with an Abelian Zq gauge field. For N-f = 2 and Q =1 we observe several transition lines that belong to the O(4), O(3), and O(2) vector universality classes, depending on the symmetry breaking pattern at the transition. The universality class is independent of q as long as q ? 3. The universality class of the transition is uniquely determined by the behavior of the scalar fields; gauge fields do not play any role. We also investigate the system for N-f = 15 and Q = 2. In the presence of U(1) gauge fields, the system undergoes transitions associated with charged fixed points of the Abelian-Higgs field theory. These continuous transitions turn into first-order ones when the U(1) gauge fields are replaced by the discrete Z(q) fields: in the present compact model charged transitions appear to be very sensitive to the nature of the gauge fields.