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We show that under tension, a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintutively, have a negative Poisson's ratio, or auxetic behavior. We derive the conditions under which the triangular lattice in two dimensions and lattices with cubic symmetry in three dimensions exhibit a negative Poisson's ratio. In the former case, the simple Lennard-Jones potential can give rise to auxetic behavior. In the latter case, negative Poisson's ratiodoi:10.1103/physrevlett.101.085501 pmid:18764632 fatcat:atmzzm54zfhsdjx5bqhekpdq6m