  By making use of some symmetry properties of the relevant Hamiltonian, two
fundamental relations between the ferromagnetic magnetization and a spin
correlation function are derived for the $d (=1,2,3)$-dimensional Hubbard model
at finite temperatures. These can be viewed as a kind of Ward-Takahashi
identities. The properties of the magnetization as a function of the applied
field are discussed. The results thus obtained hold true for both repulsive and
attractive on-site Coulomb interactions, and for arbitrary electron fillings.
