$T=0.008$ in the four-spin system. The ground-state and the first two excited-state energy levels versus $J_2$ are inserted.](next_fig1.eps){width="45.00000%"}

We now make numerical calculations of entanglement and first consider the low-temperature case. We take $J_1=1$ in all the following plots. In our system there exist three kinds of negativity, the negativity ${\cal N}_{1/2,1}$ between spin-1 and spin-1/2, ${\cal N}_{1/2,1/2}$ between two spin-1/2, and ${\cal
N}_{1,1}$ between two spin-1.

In Fig. 5, we plot the negativity versus $J_2$ in four-spin system at a low temperature of $T=0.008$. It is clear to see that ${\cal
N}_{1/2,1}$ keeps a value about $1/6$ when $J_2$ increases from zero until it reaches the critical point, at which the ${\cal
N}_{1/2,1}$ displays a jump to zero. This behavior of entanglement is consistent with that at zero temperature from the analytical results. It is natural to see that increase of NNN exchange interaction will suppress the entanglement of NN spins, and at last completely erase the entanglement.

In comparison with ${\cal N}_{1/2,1}$, the negativities ${\cal
N}_{1,1}$ and ${\cal N}_{1/2,1/2}$ behave distinctly. We see that near the point of $J_2=1/4$, ${\cal N}_{1,1}$ increases quickly to a steady value about $1/3$, and when $J_2$ reaches the value about $1/2$, ${\cal 