Abstract
The most general spin model with nearest-neighbour interactions invariant under a global Zp symmetry in two dimensions is considered. Dual transformations are discussed, and the subset of self-dual models is characterised. The phase diagrams for p>or=5 are particularly rich, containing first-order, second-order and infinite-order phase transitions. In particular, the existence of a massless phase similar to the low-temperature phase of the XY model is established.