  The magnetic properties of the two-site Hubbard cluster (dimer or pair),
embedded in the external electric and magnetic fields and treated as the open
system, are studied by means of the exact diagonalization of the Hamiltonian.
The formalism of the grand canonical ensemble is adopted. The phase diagrams,
on-site magnetization, spin-spin correlations, mean occupation numbers and
hopping energy are investigated and illustrated in figures. An influence of
temperature, mean electron concentration, Coulomb $U$ parameter and external
fields on the quantities of interest is presented and discussed. In particular,
the anomalous behaviour of the magnetization and correlation function vs.
temperature near the critical magnetic field is found. Also, the effect of
magnetization switching by the external fields is demonstrated.
