  The decoherence of quantum correlation is investigated in the Heisenberg spin
system with the asymmetric anisotropic interactions. The quantum entanglement
and discord are used to quantify the quantumness of the correlations. By the
analytical and numerical methods, we find that quantum discord decays
asymptotically in time under the effects of the independent local Markovian
reservoirs. This is markedly different from the sudden change of the
entanglement. Before the disappearance of the entanglement, the dynamic
behaviour of quantum discord is very similar to that of the entanglement. It is
also shown that the discord declines rapidly for the interacting spin system
compared with the case of noninteracting qubits. At an arbitrary finite
temperature, the nonzero thermal discord can be enhanced by the asymmetric
anisotropic interactions which induce quantum fluctuations.
