  We investigate how the interplay between a staggered magnetic field and
staggered coupling strength affects both ground state and thermal entanglement.
Upon analytically calculating thermodynamic quantities and the correlation
functions for such a system, we consider both the global Meyer-Wallach measure
of entanglement and the concurrence between pairs of spins. We discover two
quantum phase transitions present in the model and show that the quantum phase
transitions are reflected in the behaviour of the entanglement at zero
temperature. We discover that increasing the alternating field and alternating
coupling strength can actually increase the amount of entanglement present at
both zero temperature and for thermal states of the system.
