  We investigate pairwise quantum correlation as measured by the quantum
discord as well as its classical counterpart in the thermodynamic limit of
anisotropic XY spin-1/2 chains in a transverse magnetic field for both zero and
finite temperatures. Analytical expressions for both classical and quantum
correlations are obtained for spin pairs at any distance. In the case of zero
temperature, it is shown that the quantum discord for spin pairs farther than
second-neighbors is able to characterize a quantum phase transition, even
though pairwise entanglement is absent for such distances. For finite
temperatures, we show that quantum correlations can be increased with
temperature in the presence of a magnetic field. Moreover, in the XX limit, the
thermal quantum discord is found to be dominant over classical correlation
while the opposite scenario takes place for the transverse field Ising model
limit.
