Replica symmetry and massless modes in spin glasses. II. Non-Ising spins

For pt.I, see ibid., vol.12, p.79 (1979). A recent investigation of the Ising spin glass using the n to O replica method is generalised to m-vector spins. As for Ising spins (m=1), the order-parameter correlation functions contain, within mean-field theory, massless modes which become unstable at first order in perturbation theory about the mean-field solution. An alternative formulation of perturbation theory restores stability, giving massless modes once more, but yields an expansion for the order parameter which breaks down for dimensionalities d<or=4 due to infrared divergences. A dimensionality of four is therefore interpreted as the lower critical dimensionality of the theory, as for the Ising spin glass.