visualizations/ft2.md

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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