| Abstract: |
| Non-convex (short-range) interactions on lattices give rise, in a passage discrete-to-continuum, to interfacial energies such as those found in variational theories of Fracture. The details of the interfacial energy functions are usually captured by looking at the corresponding behaviour of Ising Systems. When long-range interactions are present, the topology of the interactions may give rise to non-local effects and diffuse interfaces. We consider the case when each node interacts with a substantial portion of the nodes of the lattice (dense graph), and give a description of the limit in terms of an energy defined in terms of the general notion of a limit graphon. |
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