Massless phases and symmetry restoration in abelian gauge theories and spin systems

We give a new, elementary proof for the existence of a deconfining transition to a massless (QED) phase in the four-dimensional U(1) lattice gauge theory and of an intermediate QED phase, accompanied by dynamical restoration of local U(1) invariance, in the four dimensional Zsub(N) models, with N large. Our methods can also be used to prove the existence of a phase transition in the XY model in three or more dimensions, in three- and four-dimensional abelian Higgs models, and in more general models admitting some local, abelian gauge invariance. (orig.)