Variational discussion of the Hamiltonian Z(N) spin model in 1 + 1 and 2 + 1 dimensions

We study the Z(N) spin model, as well as its limiting forms for N -> oo by means of a variational approach. We find, for 1 + 1 dimensions, the two transitions of the model separating the disordered, massless and ordered phases. In the case of 2 + 1 dimensions, we obtain only the disorder-order phase transition which implies for N ->oo a single confining phase for the dual U (l) gauge theory.