  We investigate the ground state and the thermal entanglement in the two-qubit
Ising model interacting with a site-dependent magnetic field. The degree of
entanglement is measured by calculating the concurrence. For zero temperature
and for certain direction of the applied magnetic field, the quantum phase
transition observed under a uniform external magnetic field disappears once a
very small non-uniformity is introduced. Furthermore, we have shown
analytically and confirmed numerically that once the direction of one of the
magnetic field is along the Ising axis then no entangled states can be
produced, independently of the degree of non-uniformity of the magnetic fields
on each site.
