Decay of Superconducting and Magnetic Correlations in One- and Two-Dimensional Hubbard Models

Abstract

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.