RIGOROUS BOUNDS ON THE SUSCEPTIBILITIES OF THE HUBBARD-MODEL

Rigorous bounds on the susceptibilities of the single-band Hubbard model which hold in all dimensions are presented. In the attractive model the spin susceptibility is bounded above by (4U)-1 where U(<0) is the on-site interaction potential. In the half-filled repulsive model on a bipartite lattice the charge and the on-site pairing susceptibilities are bounded above by U-1. The present result implies that the susceptibilities never diverge in the above mentioned circumstances and also the absence of corresponding long-range order. © 1990 The American Physical Society.