Decay of correlations in N-vector ferromagnetic quantum models with long-range interactions

A lattice model of N-vector quantum anharmonic oscillators with long-range attraction is studied. This model is characterized by the critical temperature T-C(N) >= 0. By means of the Hammersley-Lieb-Simon inequality and a path integral representation of the two-point correlation function g(N), we prove that, for T > T-C(1) >= T-C(N), up to a constant this function is bounded from above by the interaction intensity. The decay of the two-point correlation function of the corresponding classical model is also discussed.