Interfacial energies on quasicrystals

We consider nearest-neighbour ferromagnetic energies defined on a quasicrystal modeled following the so-called cut-and-project approach as a portion of a regular lattice contained in a possibly irrational stripe defined as a neighborhood of a k-dimensional subspace in an n-dimensional space. The overall properties of this system are described by an effective surface energy on a k-dimensional space obtained as Γ-limit of the scaled discrete energies. © 2012 The authors.