  We study the long-range quantum correlations in the anisotropic XY-model. By
first examining the thermodynamic limit we show that employing the quantum
discord as a figure of merit allows one to capture the main features of the
model at zero temperature. Further, by considering suitably large site
separations we find that these correlations obey a simple scaling behavior for
finite temperatures, allowing for efficient estimation of the critical point.
We also address ground-state factorization of this model by explicitly
considering finite size systems, showing its relation to the energy spectrum
and explaining the persistence of the phenomenon at finite temperatures.
Finally, we compute the fidelity between finite and infinite systems in order
to show that remarkably small system sizes can closely approximate the
thermodynamic limit.
