{
  "id": "1701.04482",
  "version": "v1",
  "published": "2017-01-16T22:53:21.000Z",
  "updated": "2017-01-16T22:53:21.000Z",
  "title": "Asymptotic behaviour of ground states for mixtures of ferromagnetic and antiferromagnetic interactions in a dilute regime",
  "authors": [
    "Andrea Braides",
    "Andrea Causin",
    "Andrey Piatnitski",
    "Margherita Solci"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We consider randomly distributed mixtures of bonds of ferromagnetic and antiferromagnetic type in a two-dimensional square lattice with probability $1-p$ and $p$, respectively, according to an i.i.d. random variable. We study minimizers of the corresponding nearest-neighbour spin energy on large domains in ${\\mathbb Z}^2$. We prove that there exists $p_0$ such that for $p\\le p_0$ such minimizers are characterized by a majority phase; i.e., they take identically the value $1$ or $-1$ except for small disconnected sets. A deterministic analogue is also proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-16T22:53:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ground states",
      "antiferromagnetic interactions",
      "dilute regime",
      "asymptotic behaviour",
      "two-dimensional square lattice"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}