maxima. So it is clear that there also exists a threshold $J_\text{2th}$ corresponding to the boundary between zero and nonzero negativities.

![Negativity ${\cal N}_{1/2,1}$ versus both the exchange interaction coefficient $J_2$ and the temperature in the four-spin system.](next_fig4.eps){width="45.00000%"}

In Fig. 6, we show the negativity ${\cal N}_{1/2,1}$ versus the temperature and $J_2$. When the temperature approaches zero, the ${\cal N}_{1/2,1}$ reaches its maximum, and then with the temperature increasing, ${\cal N}_{1/2,1}$ decreases to zero. On the $J_2-T$ plane, there is a curve along which the negativity just turns to be zero. It is possible to consider that the curve describes the threshold $J_\text {2th}$ versus the temperature. Obviously, $J_\text {2th}$ does not behave as a monotonous function of the temperature, and it displays a peak at about $T=0.178$, This behavior is in big contrast with the case of non-mixed qubit systems [@Gu]. When the temperature rises, the weight of excited states will increase and it may strongly affect the negativity. This behavior of $J_\text {2th}$ results from both the mixture of excited states to the thermal state and the intrinsic properties of the mixed-spin system. In addition, after crossing the temperature about $T=1.082$, ${\cal N}_{1/2,1}$ will vanish, irrespective of the 