Crystallinity of the Homogenized Energy Density of Periodic Lattice Systems
Crystallinity of the Homogenized Energy Density of Periodic Lattice Systems
.We study the homogenized energy densities of periodic ferromagnetic Ising systems. We prove that, for finite range interactions, the homogenized energy density, identifying the effective limit, is crystalline, i.e., its Wulff crystal is a polytope, for which we can (exponentially) bound the number of vertices. This is achieved by deriving …