  In this paper we consider a class of the 2D integrable models. These models
are higher spin XXZ chains with an extra condition of the commensurability
between spin and anisotropy. The mathematics underlying this commensurability
is provided by the quantum groups with 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 N=2
supersymmetric Sine-Gordon matrix and an RSOS piece. The physics of the N odd
case is rather different. Here, the supersymmetry does not manifest itself and
the bootstrap hypothesis fails. Away from the commensurable point, we find an
unusual behaviour. The magnetization of our chains depends on the sign of the
external magnetic field.
