Upper bounds for ground-state correlation functions in the Hubbard model

We present rigorous bounds on the ground-state spin and charge correlation functions of the single-band Hubbard model defined on a bipartite lattice. In the attractive case, the spin correlation function is bounded from above by a quantity depending only on the value of the Coulomb interaction. A similar result is obtained in the half-filled repulsive model when the charge and the on-site pairing correlation functions are considered. The present results imply that the related susceptibilities never diverge and the absence of corresponding long-range orders.