We show that spin systems with infinite-range interactions can violate at thermal equilibrium a multipartite Bell inequality, up to a finite critical temperature $T_c$. Our framework can be applied to a wide class of spin systems and Bell inequalities, to study whether nonlocality occurs naturally in quantum many-body systems close to the ground state. Moreover, we also show that the low-energy spectrum of the Bell operator associated to such systems can be well approximated by the one of a quantum harmonic oscillator, and that spin-squeezed states are optimal in displaying Bell correlations for such Bell inequalities.
 J. S. Bell, Physics 1, 195 (1964).
 S. Pironio, A. Acín, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, Nature 464, 1021 (2010).
 D. Mayers and A. Yao, Quantum Information & Computation 4, 273 (2004).
 B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, Nature Chemistry 2, 106 (2010), article.
 D. Liu, S.-J. Ran, P. Wittek, C. Peng, R. B. García, G. Su, and M. Lewenstein, ``Machine learning by two-dimensional hierarchical tensor networks: A quantum information theoretic perspective on deep architectures,'' (2017), arXiv:1710.04833.
 A. Salles, D. Cavalcanti, A. Acin, D. Perez-Garcia, and M. M. Wolf, Quantum Information and Computation 10, 0703 (2010).
 A. Harrow, Applications of coherent classical communication and the Schur transform to quantum information theory, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA (2005).
 K. Audenaert, ``A digest on representation theory of the symmetric group,'' (2006).
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