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We show that the bipartite logarithmic entanglement negativity (EN) ofquantum spin models obeys an area law at all nonzero temperatures. We developnumerical linked cluster (NLC) expansions for the `area-law' logarithmicentanglement negativity as a function of temperature and other parameters. Forone-dimensional models the results of NLC are compared with exactdiagonalization on finite systems and are found to agree very well. The NLCresults are also obtained for two dimensional XXZ and transverse-field Isingmodels. In all cases, we find a sudden onset (or sudden death) of negativity ata finite temperature above which the negativity is zero. We use perturbationtheory to develop a physical picture for this sudden onset (or sudden death).The onset of EN or its magnitude are insensitive to classicalfinite-temperature phase transitions, supporting the argument for absence ofany role of quantum mechanics at such transitions. On approach to a quantumcritical point at $T=0$, negativity shows critical scaling in size andtemperature.

Nonzero temperature Entanglement Negativity of quantum spin models: Area law, Linked Cluster Expansions and Sudden Death