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.

5 pages 3 figures