  In a general class of one and two dimensional Hubbard models, we prove upper
bounds for the two-point correlation functions at finite temperatures for
electrons, for electron pairs, and for spins. The upper bounds decay
exponentially in one dimension, and with power laws in two dimensions. The
bounds rule out the possibility of the corresponding condensation of
superconducting electron pairs, and of the corresponding magnetic ordering. Our
method is general enough to cover other models such as the t-J model.
