FERRO-MAGNETIZATIONS AND ANTIFERRO-MAGNETIZATIONS IN RSOS MODELS

We study a class of restricted solid-on-solid (RSOS) models related to the quantum group U(q)(sl(n)) with q a general primitive root of unity. Physical regimes of the models enjoy intriguing equivalence properties under the interchange of the rank n and the relevant level of the affine Lie algebra A(n-1)(1) (level-rank duality) and also the q- and q-1-deformations (q +/- 1 duality). By using these we give a classification scheme for ferromagnetic and antiferromagnetic orderings at low temperature. We also propose that the level-rank duality is inherited in rational Toda field theories with imaginary coupling constants. This explains the deficiency structure of the conserved currents in a series of deformed non-unitary conformal field theories.