Negative Poisson's ratio materials via isotropic interactions
  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. 
Mikael C. Rechtsman, Frank H. Stillinger, and Salvatore Torquato