  Quantum and classical pairwise correlations in two typical collective spin
systems (i.e., the Dicke model and the Lipkin-Meshkov-Glick model) are
discussed. These correlations in the thermodynamical limit are obtained
analytically and in a finite-size system are calculated numerically. Large-size
scaling behavior for the quantum discord itself is observed, which has never
been reported in another critical system. A logarithmic diverging behavior for
the first derivative of the quantum discord is also found in both models, which
might be universal in the second-order quantum phase transition. It is
suggested that the pronounced maximum or minimum of first derivative of quantum
discord signifies the critical point. Comparisons between the quantum discord
and the scaled concurrence are performed. It is shown that the quantum discord
is very small in one phase and robust in the other phase, while the scaled
concurrence shows maximum at the critical point and decays rapidly when away
from the the critical point.
