  Entanglement of dipole-dipole interacting spins 1/2 is usually investigated
when the energy of interaction with an external magnetic field (the Zeeman
energy) is greater than the energy of dipole interactions by three orders.
Under this condition only a non-equilibrium state of the spin system, realized
by pulse radiofrequence irradiations, results in entanglement. The present
paper deals with the opposite case: the dipolar interaction energy is the order
of magnitude or even larger than the Zeeman one. It was shown that entanglement
appears under the thermodynamic equilibrium conditions and the concurrence
reaches the maximum when the external field is directed perpendicular to the
vector connecting the nuclei. For this direction of the field and a system of
two spins with the Hamiltonian accounting the realistic dipole-dipole
interactions in low external magnetic field, the exact analytical expression
for concurrence was also obtained. The condition of the entanglement appearance
and the dependence of concurrence on the external magnetic field, temperature,
and dipolar coupling constant were studied.
