  The chemical potential of the two-site Hubbard cluster (pair) embedded in the
external electric and magnetic fields is studied by exact diagonalization of
the Hamiltonian. The formalism of the grand canonical ensemble is adopted. The
influence of temperature, Hubbard on-site Coulombic energy $U$ and electron
concentration on the chemical potential is investigated and illustrated in
figures. In particular, a discontinuous behaviour of the chemical potential (or
electron concentration) in the ground state is discussed.
