  Bell inequalities define experimentally observable quantities to detect
non-locality. In general, they involve correlation functions of all the
parties. Unfortunately, these measurements are hard to implement for systems
consisting of many constituents, where only few-body correlation functions are
accessible. Here we demonstrate that higher-order correlation functions are not
necessary to certify nonlocality in multipartite quantum states by constructing
Bell inequalities from one- and two-body correlation functions for an arbitrary
number of parties. The obtained inequalities are violated by some of the Dicke
states, which arise naturally in many-body physics as the ground states of the
two-body Lipkin-Meshkov-Glick Hamiltonian.
