01090nas a2200121 4500008004100000245009000041210006900131520064600200100002300846700002400869700002400893856005100917 2017 en d00aOn the effect of interactions beyond nearest neighbours on non-convex lattice systems0 aeffect of interactions beyond nearest neighbours on nonconvex la3 aWe 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.1 aAlicandro, Roberto1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://urania.sissa.it/xmlui/handle/1963/35268