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We study the classical correlation (CC) and quantum discord (QD) between twospin subgroups of the Lipkin-Meshkov-Glick (LMG) model in both binary andtrinary decompositions of spins. In the case of bipartition, we find that theclassical correlations and all the quantum correlations including the QD, theentanglement of formation (EoF) and the logarithmic negativity (LN) aredivergent in the same singular behavior at the critical point of the LMG model.In the case of tripartition, however, the classical correlation is stilldivergent but all the quantum correlation measures remain finite at thecritical point. The present result shows that the classical correlation is veryrobust but the quantum correlation is much frangible to the environmentdisturbance. The present result may also lead to the conjecture that theclassical correlation is responsible for the singularity behavior of physicsquantities at critical points of a many-body quantum system.

Singularity of classical and quantum correlations at critical points of the Lipkin-Meshkov-Glick model in bipartition and tripartition of spins