  The charge spin-separation, pseudogap formation and phase diagrams are
studied in two and four site Hubbard clusters using analytical diagonalization
and grand canonical ensemble method in a multidimensional parameter space of
temperature, magnetic field, on-site Coulomb interaction ($U\ge 0$), and
chemical potential. The numerically evaluated, exact expressions for charge and
spin susceptibilities provide clear evidence for the existence of true gaps in
the ground state and pseudogaps in a limited range of temperature.
  In particular, Mott-Hubbard type charge crossover, spin pseudogap and
magnetic correlations with antiferromagnetic (spin) pseudogap structure for two
and four site clusters closely resemble the pseudogap phenomena and the
normal-state phase diagram in high T$_c$ superconductors. ~ ~
