SPIN ANISOTROPY COMMENSURABLE CHAINS - QUANTUM GROUP SYMMETRIES AND N=2 SUSY

In this paper we consider a class of 2D integrable models. These models are higher-spin XXZ-chains with an extra condition of the commensurability between spin (j) and anisotropy (gamma): sin gamma (2j + 1) = 0. Thus, the mathematics underlying this commensurability is provided by the quantum groups with the deformation parameter being an Nth root of unity. Our discussion covers a range of topics including new integrable deformations, thermodynamics, conformal behaviour, S-matrices and magnetization. The emerging picture strongly depends on the N-parity. For the N-even case at the commensurable point, S-matrices factorize into an N = 2 supersymmetric sine-Gordon matrix and an RSOS piece. The physics of the N-odd case is rather different. Here, there are hints suggesting that supersymmetry is still present, however we did not unravel its nature, yet. In this case, S-matrices factorize into two RSOS pieces. The second RSOS piece has dependence on an extra parameter. Away from the commensurable point, we find an unusual magnetic behaviour. The magnetization of our chains depends on the sign of the external magnetic field.