The thermal pairwise entanglement (TE) of the S=1/2 XY chain in a transversemagnetic field is exactly resolved by means of the Jordan-Wignertransformation. It is found that the TE vanishes at a common temperatureTc~0.4843J, which is irrelevant to the field. A thermal quantity is proposed towitness the entangled state. Furthermore, the TE of the S=1/2antiferromagnetic-ferromagnetic (AF-F) Heisenberg chain is studied by thetransfer-matrix renormalization group method.The TEs of the spins coupled by AFand F interactions are found to behave distinctively. The vanishing temperatureof the field-induced TE of the spins coupled by F interactions is observed tochange with the magnetic field. The results are further confirmed and analyzedby the mean-field theory.
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