D-COMPONENT ROTATORS AS THE CLASSICAL LIMIT OF QUANTUM SO(D) VECTOR MODELS

The author considers a class of spin systems whose single-site configuration space is an orbit of a representation of a compact Lie group G. For these models the author gets upper and lower bounds to the quantum partition function in terms of two classical partition functions. If a certain group-theoretic condition is satisfied, then these bounds allow one to prove the convergence of a suitable sequence of quantum partition functions to the 'corresponding' classical one. This condition is shown to be satisfied, in particular, for the D-component rotators when D is odd. The result could be useful for the extension of the Lee-Yang theorem to such models.