| temperature \(T_{\text{in}}\) versus different \(J_{\text{in}}\) from the curve in the \(J_{\text{in}}\) - \(T\) plane. When \(J_{\text{in}}\) increases, \(T_{\text{in}}\) decreases, and when \(J_{\text{in}}\) crosses about \(0.375\), \(N_{\text{in}}\) will disappear at any temperature. Next, we consider the entanglement between NN spins. In Fig. 7, we plot the negativity \(N_{\text{in}}\) as a func- tion of the temperature and \(J_{\text{in}}\). We can see that, before \(J_{\text{in}}\) reaches the value about \(J_{\text{in}}\) = 0.5, \(N_{\text{in}}\) increases and the region \(N_{\text{in}}\) is enhanced by the increasing NN interaction. This is a result from the competition of two kinds of exchange interactions. The thermal fluctuation all along suppresses the entanglement. So, from the curve lying on the \(J_{\text{in}}\) - \(T\) plane which corresponds to the boundary of the nonzero and zero values of \(N_{\text{in}}\), we may find that the higher the temperature is, the larger the threshold \(J_{\text{in}}\) will be. From another point of view, the \(T_{\text{in}}\) increases as \(J_{\text{in}}\) increases. In Fig. 8, we plot the negativity \(N_{\text{in}}\) versus \(T\) and \(J_{\text{in}}\). In the region of \(J_{\text{in}}\) < 0.25, the increasing NN exchange interaction \(J_{\text{in}}\) enhances the negativity and exhibits two particular fla
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