[en] We study the Z(N) spin model, as well as its limiting forms for N → infinity by means of a variational approach. We find for 1+1 dimensions a signal of one disorder-massless and one massless-order phase transition, and in 2+1 dimensions evidence for a disorder-order transition. A possible massless-order transition which appears with some ansatz in the latter case is ruled out by other trial states with lower energy. (author)