  Bell nonlocality, entanglement and nonclassical correlations are different
aspects of quantum correlations for a given state. There are many methods to
measure nonclassical correlations. In this paper, nonclassical correlations in
two-qubit spin models are measured by use of measurement-induced disturbance
(MID) [Phys. Rev. A, 77, 022301 (2008)] and geometric measure of quantum
discord (GQD) [Phys. Rev. Lett. 105, 190502 (2010)]. Their dependencies on
external magnetic field, spin-spin coupling, and Dzyaloshinski-Moriya (DM)
interaction are presented in detail. We also compare Bell nonlocality,
entanglement measured by concurrence, MID and GQD and illustrate their
different characteristics.
