  The effects of mixedness and entanglement on the lower bound and tightness of
the entropic uncertainty in the Heisenberg model with Dzyaloshinski-Moriya (DM)
interaction have been investigated. It is found that the mixedness can reflect
the essence of the entropic uncertainty better than the entanglement.
Meanwhile, the uncertainty of measurement results will be reduced by the
entanglement and improved by the mixedness.The entanglement can destroy the
tightness of the uncertainty, while the tightness will be improved with the
increasing of the mixedness. In addition, the tightness of the uncertainty in
Heisenberg model can be expressed as a function of the magnetic properties, the
strength of the DM interaction as well as the mixedness of the state and the
functional form has no relationship with temperature. What's more, the entropic
uncertain inequality becomes uncertain equality when the mixedness of the
system reach the minimum value.For a given mixedness, the tightness will be
reduced with the increasing of the strength of DM interaction at the
antiferromagnetic case while the situation is just the opposite for the
ferromagnetic case.
