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Quantum discord is a measure of quantum correlations which is not equivalent to the standard measures of entanglement in the case of mixed quantum states: It can be non-zero even when entanglement vanishes. Interest on the discord has been triggered by the recent discovery that it may be responsible for the exponential speedup obtained in certain quantum algorithms based on mixed quantum states (mixed state quantum computation), where entanglement is negligible. In this contribution we describe the quantum discord and evaluate this quantity exactly for typical states of spin pairs in a spin chain with XY Heisenberg couplings in a transverse field [1]. It is shown that its behavior can differ considerably from that of the pairwise entanglement at low fields, reaching full range in the vicinity of special critical points. We also discuss possible entropic generalizations of this measure, which could simplify the evaluation in general systems yet detecting the same type of correlations. [1] L. Ciliberti, R. Rossignoli, N. Canosa, Phys. Rev. A 82, 042316 (2010); Phys. Rev. A 82, 052342 (2010).