  We perform an extensive study of the properties of global quantum
correlations in finite-size one-dimensional quantum spin models at finite
temperature. By adopting a recently proposed measure for global quantum
correlations [C. C. Rulli, and M. S. Sarandy, Phys. Rev. A, 84, 042109 (2011)],
called global discord, we show that critical points can be neatly detected even
for many-body systems that are not in their ground state. We consider the
transverse Ising model, the cluster-Ising model where three-body couplings
compete with an Ising-like interaction, and the nearest-neighbor XX Hamiltonian
in transverse magnetic field. These models embody our canonical examples
showing the sensitivity of global quantum discord close to criticality. For the
Ising model, we find a universal scaling of global discord with the critical
exponents pertaining to the Ising universality class.
