  We study the entanglement distillability properties of thermal states of
many-body systems. Following the ideas presented in [D.Cavalcanti et al.,
arxiv:0705.3762], we first discuss the appearance of bound entanglement in
those systems satisfying an entanglement area law. Then, we extend these
results to other topologies, not necessarily satisfying an entanglement area
law. We also study whether bound entanglement survives in the macroscopic limit
of an infinite number of particles.
