Statistical mechanics of quantum spin systems

The thermodynamic limit of a quantum spin system is considered. It is demonstrated that for a large class of interactions and a wide range of the thermodynamic parameters the equilibrium state of the system is describable by an extremalZv-invariant state (a single phase state) over aC* algebra of local observables. It is further shown that the equilibrium state may be obtained as the solution of a variational problem involving the mean entropy. These results extend results previously obtained for classical spin systems byGallavotti, Miracle-Sole andRuelle.