Abstract
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 Eε has the form
. The cases of homogenization and of non-pairwise interacting systems (e.g. multiple-exchange spin systems) are also discussed.
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Recommended by J Lega