affect the negativity.

### Entanglement versus $J_2$ and $T$

![Negativity ${\cal N}_{1/2,1}$ versus both the exchange interaction $J_2$ and the temperature in the six-spin system.](next_fig7.eps){width="45.00000%"}

![Negativity ${\cal N}_{1,1}$ versus both the exchange interaction $J_2$ and the temperature in six-spin system.](next_fig8.eps){width="45.00000%"}

Now, we present the entanglement versus $J_2$ and $T$ in the six-spin model. The NN negativity ${\cal N}_{1/2,1}$ is shown in Fig. 11. On the $J_2-T$ plane, similar to the four-spin case, the $J_\text {2th}$ does not behave as a monotonous function of $T$ and it reaches its maximum at about $T=0.27$. From the figure, we may find that the entanglement only exists in the region approximately $T<0.925$ and $J_2<0.418$. The strong NNN interaction and thermal fluctuation will suppress the NN entanglement to zero.

We do not plot the negativity ${\cal N}_{1/2,1/2}$ as it is zero all along for any $J_2$ and $T$. We give the NNN negativity ${\cal
N}_{1,1}$ in Fig. 12. In the region of $J_2<0.282$, there is no negativity ${\cal N}_{1,1}$ at any temperature. The threshold $J_\text {2th}$ is increased by the increasing temperature, similar to the four-spin case.

conclusion
==========

In conclusion, we have studied the entanglement properties of the (1/2,1) mixed-spin systems described by the 