TY - RPRT T1 - On the effect of interactions beyond nearest neighbours on non-convex lattice systems Y1 - 2017 A1 - Roberto Alicandro A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro AB - We analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation. UR - http://urania.sissa.it/xmlui/handle/1963/35268 U1 - 35574 U2 - Mathematics U4 - 1 ER -