PROOF OF ANTIFERROMAGNETISM IN THE HALF-FILLED HUBBARD-MODEL IN INFINITE DIMENSIONS

We obtain a rigorous condition for the divergence of the staggered sus ceptibility of the half filled Hubbard model in infinite dimensions by differentiating the exact functional-integral equation for the local Greens function with respect to a staggered magnetic field. In the wea k-coupling regime, we make the reasonable assumption that the high tem perature phase without broken symmetry is a Fermi liquid, and proof th at the system develops long-range antiferromagnetic order at a finite temperature.