Classical spin models with a discrete abelian symmetry (Zp) are studied and compared to analogous models with a continuous (0(2)) symmetry.
The dependence on p (the number of states) of some quantities, e.g ., the pressure and correlation functions, is studied. For high p, under fairly general conditions, the pressure of the Zp invariant model converges exponentially, in p, to that of the 0(2) model. Results of a similar nature, although obtained under more restrictive conditions, are presented for a class of expectation values.
Several different methods of proving Mermin- and Wagner-like results are reviewed and it is suggested that these methods are not sufficiently powerful to be used in obtaining upper bounds on the magnetization temperature of the two dimensional Zp model. A rigorous lower bound is obtained using a Peierls-Chessboard method.
