  It is known from the analysis of the density matrix for bipartite systems
that the quantum discord (as a measure of quantum correlations) depends on the
particular subsystem chosen for the projective measurements. We study asymmetry
of the discord in a simple physical model of two spin-1/2 particles with the
dipole-dipole interaction governed by the XY Hamiltonian in the inhomogeneous
magnetic field. The dependence of the above discord asymmetry on the Larmour
frequencies at both T=0 (the ground state) and $T>0$ has been investigated. It
is demonstrated, in particular, that the asymmetry is negligible for high
temperatures but it may become significant with the decrease in temperature.
