Noncompact lattice Higgs model with Abelian discrete gauge groups: Phase diagram and gauge symmetry enlargement

We study the phase diagram and phase transitions of the three dimensional multicomponent lattice Higgs model with noncompact Abelian discrete groups. The model with noncompact U(1) gauge group is known to undergo, for a sufficiently large number of scalar fields N, a continuous transition associated to the charged fixed point of the continuous Abelian Higgs field theory. We show that in the model with gauge group Z(nc) q equivalent to 2 pi Z/q only critical transitions in the orthogonal universality classes are present for small values of N, while a symmetry enlargement to the continuous Abelian Higgs universality class happens when q 5 and N is large enough.