Global thermal entanglement in n-qubit systems

We examine the entanglement of thermal states of n spins interacting through different types of XY couplings in the presence of a magnetic field, by evaluating the negativities of all possible bipartite partitions of the whole system and of subsystems. We consider both the case where every qubit interacts with all others and where just nearest neighbors interact in a one-dimensional chain. Limit temperatures for non-zero negativities are also evaluated and compared with the mean field critical temperature. It is shown that limit temperatures of global negativities are strictly independent of the magnetic field in all XXZ models, in spite of the quantum transitions that these models may exhibit at zero temperature, while in anisotropic models they always increase for sufficiently large fields. Results also show that these temperatures are higher than those limiting pairwise entanglement.