In this paper, theorems are proved concerning the total spin and the s
ign of the spin-spin correlation function for positive (semi)definite
states of correlated electrons at half filling. These theorems are app
lied to the ground states of the Anderson model, the Kondo model, and
a generalized Hubbard model for ferromagnetism. It is found that there
exists ferromagnetic or antiferromagnetic long-range order in several
cases.