{
  "id": "1612.02775",
  "version": "v1",
  "published": "2016-12-08T19:10:02.000Z",
  "updated": "2016-12-08T19:10:02.000Z",
  "title": "Continuum limit and stochastic homogenization of discrete ferromagnetic thin films",
  "authors": [
    "Andrea Braides",
    "Marco Cicalese",
    "Matthias Ruf"
  ],
  "comment": "43 pages, 2 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the discrete-to-continuum limit of ferromagnetic spin systems when the lattice spacing tends to zero. We assume that the atoms are part of a (maybe) non-periodic lattice close to a flat set in a lower dimensional space, typically a plate in three dimensions. Scaling the particle positions by a small parameter $\\varepsilon>0$ we perform a $\\Gamma$-convergence analysis of properly rescaled interfacial-type energies. We show that, up to subsequences, the energies converge to a surface integral defined on partitions of the flat space. In the second part of the paper we address the issue of stochastic homogenization in the case of random stationary lattices. A finer dependence of the homogenized energy on the average thickness of the random lattice is analyzed for an example of magnetic thin system obtained by a random deposition mechanism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-08T19:10:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J45",
      "49J55",
      "49S05",
      "82B20",
      "82B24",
      "49Q20"
    ],
    "keywords": [
      "discrete ferromagnetic thin films",
      "stochastic homogenization",
      "continuum limit",
      "ferromagnetic spin systems",
      "random deposition mechanism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}