  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 ratio can be exhibited even when the material is
constrained to be elastically isotropic.
