We have investigated the multipartite nonlocality and global quantum discord (GQD) in the antiferromagnetic Lipkin-Meshkov-Glick (LMG) model. We find that nonlocality and GQD can indicate quantum phase transitions by singular behaviors. The results also show that GQD always behaves a linear growth with ${log}_{10}N$ in the LMG model, which is different from linear scaling in one-dimensional chains. And this scaling behavior is not affected by anisotropic parameter $\gamma$. Moreover, the nonlocality (denoted by $\mathcal{S}$) is discovered to scale as ${log}_{10}S{|}_h\sim aN+b$ for the transverse-field LMG model (i.e., $\gamma =0$). However, scaling behaviors can be well fitted by formula $S{|}_h=a\frac{1}{N}+b$ for the LMG model with $\gamma >0$. By comparing the results of GQD and nonlocality, we have observed that nonlocality decreases but GQD increases as the size of the system grows. These results indicate that $\gamma$ has a significant influence on the nonlocality and GQD in the LMG model.

我们已经研究了反铁磁Lipkin-Meshkov-Glick（LMG）模型中的多部分非局部性和全局量子不一致性（GQD）。我们发现非局部性和GQD可以通过奇异行为指示量子相变。结果还表明，GQD始终表现为线性增长${日志}_{10}ñ$在LMG模型中，它不同于一维链中的线性缩放。而且这种缩放行为不受各向异性参数的影响$\gamma$。此外，非本地性（用$\mathcal{小号}$）被发现按比例缩放 ${日志}_{10}\mathrm{小号}{|}_H〜\mathrm{一种}ñ+b$ 对于横向场LMG模型（即， $\gamma =0$）。但是，缩放行为可以通过公式很好地拟合$\mathrm{小号}{|}_H=\mathrm{一种}\frac{\mathrm{1个}}{ñ}+b$ 用于LMG模型 $\gamma >0$。通过比较GQD和非局部性的结果，我们观察到非局部性会减少，但GQD会随着系统规模的增长而增加。这些结果表明$\gamma$ 对LMG模型中的非局部性和GQD具有重大影响。