  Using Bell-inequalities as a tool to explore non-classical physical
behaviours, in this paper we analyze what one can expect to find in many-body
quantum physics. Concretely, framing the usual correlation scenarios as a
concrete spin-lattice, we want to know whether or not it is possible to violate
a Bell-inequality restricted to this scenario. Using clustering theorems, we
are able to show that a large family of quantum many-body systems behave almost
locally, violating Bell-inequalities (if so) only by a non-significant amount.
We also provide examples, explain some of our assumptions via counter-examples
and present all the proofs for our theorems. We hope the paper is
self-contained.
