  We solve analytically the $N\times N$ square lattice Hubbard model for even
$N$ at half filling and weak coupling by a new approach. The exact ground state
wave function provides an intriguing and appealing picture of the
antiferromagnetic order. Like at strong coupling, the ground state has total
momentum $K_{tot}=(0,0)$ and transforms as an $s$ wave for even $N/2$ and as a
$d$ wave otherwise.
