  We study pairwise thermal entanglement in three-qubit Heisenberg models and
obtain analytic expressions for the concurrence. We find that thermal
entanglement is absent from both the antiferromagnetic $XXZ$ model, and the
ferromagnetic $XXZ$ model with anisotropy parameter $\Delta\ge 1$. Conditions
for the existence of thermal entanglement are discussed in detail, as is the
role of degeneracy and the effects of magnetic fields on thermal entanglement
and the quantum phase transition. Specifically, we find that the magnetic field
can induce entanglement in the antiferromagnetic $XXX$ model, but cannot induce
entanglement in the ferromagnetic $XXX$ model.
