Hubbard pair cluster in the external fields. Studies of the chemical potential

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.