Variational description of bulk energies for bounded and unbounded spin systems
Roberto Alicandro, Marco Cicalese, Alberta M. Gloria · Nonlinearity · 2008
We study the asymptotic behaviour of a general class of discrete energies defined on functions of the form , as the mesh size ε goes to 0. We prove that under general assumptions that cover the case of bounded and unbounded spin systems in the thermodynamic limit, the variational limit of E ε has the form . The cases of homogenization and of non-pairwise interacting systems (e.g. multiple-exchange spin systems) are also discussed.