We examine the quantum discord between two spins in the exact ground state of finite spin-1/2 arrays with anisotropic $\mathit{XY}$ couplings in a transverse field $B$. It is shown that in the vicinity of the factorizing field $B_s$, the discord approaches a common finite non-negligible limit which is independent of the pair separation and the coupling range. An analytic expression of this limit is provided. The discord of a mixture of aligned pairs in two different directions, crucial for the previous results, is analyzed in detail, including the evaluation of coherence effects, relevant in small samples and responsible for a parity splitting at $B_s$. Exact results for finite chains with first-neighbor and full-range couplings and their interpretation in terms of such mixtures are provided.

• Received 26 July 2010

DOI:https://doi.org/10.1103/PhysRevA.82.042316