SPHERICAL LIMIT OF THE N-VECTOR MODEL AND CORRELATION INEQUALITIES

The asymptotics of the state of the n-vector model with a finite number of spins in the spherical limit is studied. Besides re-deriving the limit of the free energy, corresponding to a generalised spherical model (with 'spherical constraint' at every site), the authors also obtain the limit of the correlation functions, which allows a precise definition of the state of the latter model. Correlation inequalities are proved for ferromagnetic interactions in the asymptotic regime. In particular, it is shown that the generalised spherical model fulfils the expected Griffiths-type inequalities, differing in this respect from the spherical model with overall constraint.