q--Magnetism at roots of unity

Abstract

We study the thermodynamic properties of a family of integrable 1D spin chain hamiltonians associated with quantum groups at roots of unity. These hamiltonians depend for each primitive root of unit on a parameter $s$ which plays the role of a continuous spin. The model exhibits ferrimagnetism even though the interaction involved is between nearest neighbors. The latter phenomenon is interpreted as a genuine quantum group effect with no ``classical" analog. The discussion of conformal properties is given.