  The quantum discord, which quantifies the amount of quantum correlations
present between parts of a system, is investigated for antiferromagnetic spin
systems. The discord for a pair of spins in the many-spin ground state is
related to the diagonal and off-diagonal spin-spin correlation functions and
the local magnetization. For isotropic and translationally invariant states,
the discord is shown to be a function of the diagonal correlation function
only. Thus, near a thermal/quantum critical point, the discord for a pair of
spins shows long-range behavior, analogously of the correlation function. The
discord exhibits a kink singularity as a function of the anisotropy parameter
for the the ground state of the Heisenberg model, for both nearest-neighbor
spins as well as for well-separated spins. The preferred measurement basis for
the minimum conditional entropy, which determines the discord, changes
discontinuously across the critical point. The conditional entropy distribution
over all possible the measurement basis is investigated. For the isotropic
model, the distribution is just a delta-function, whereas it has a twin-peak
structure for anisotropic model. It is shown that the average value and the
mean-square fluctuation of the conditional entropy also show a signature of the
critical-point behavior.
