  We address the presence of bound entanglement in strongly-interacting spin
systems at thermal equilibrium. In particular, we consider thermal graph states
composed of an arbitrary number of particles. We show that for a certain range
of temperatures no entanglement can be extracted by means of local operations
and classical communication, even though the system is still entangled. This is
found by harnessing the independence of the entanglement in some bipartitions
of such states with the system's size. Specific examples for one- and
two-dimensional systems are given. Our results thus prove the existence of
thermal bound entanglement in an arbitrary large spin system with finite-range
local interactions.
