  By use of the conservation laws a four-site Hubbard model coupled to a
particle bath within an external magnetic field in z-direction was
diagonalized. The analytical dependence of both the eigenvalues and the
eigenstates on the interaction strength, the chemical potential and magnetic
field was calculated. It is demonstrated that the low temperature behaviour is
determined by a delicate interplay between many-particle states differing in
electron number and spin if the electron density is away from half-filling. The
grand partition sum is calculated and the specific heat, the suszeptibility as
well as various correlation functions and spectral functions are given in
dependence of the interaction strength, the electron occupation and the applied
magnetic field. Furthermore, for both the grand canonical and the canonical
ensemble the so called crossing points of the suszeptibility are calculated.
They confirm the universal value predicted by Vollhardt [1].
