{
  "id": "1406.3293",
  "version": "v2",
  "published": "2014-06-12T17:26:22.000Z",
  "updated": "2014-10-29T15:33:52.000Z",
  "title": "Phase transitions in layered systems",
  "authors": [
    "Luiz Renato Fontes",
    "Domingos H. U. Marchetti",
    "Immacolata Merola",
    "Errico Presutti",
    "Maria Eulalia Vares"
  ],
  "comment": "17 pages. Final version. Published in Journal of Statistical Physics (2014), volume 157, 407-421",
  "journal": "J Stat Phys 157, 2014, 407-421",
  "doi": "10.1007/s10955-014-1090-z",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the Ising model on the two-dimensional square lattice where on each horizontal line, called \"layer\", the interaction is given by a ferromagnetic Kac potential with coupling strength $J_\\gamma(x,y)=\\gamma J(\\gamma(x-y))$, where $J(\\cdot)$ is smooth and has compact support; we then add a nearest neighbor ferromagnetic vertical interaction of strength $\\gamma^{A}$ (where $A\\ge 2$ is fixed) and prove that for any $\\beta$ (inverse temperature) larger than the mean field critical value there is a phase transition for all $\\gamma$ small enough.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-12T17:26:22.000Z",
      "abstract": "We consider the Ising model on the two-dimensional square lattice where on each horizontal line, called \"layer\", the interaction is given by a ferromagnetic Kac potential with coupling strength $J_\\gamma(x,y)=\\gamma J(\\gamma(x-y))$, where $J(\\cdot)$ is smooth and has compact support; we then add a nearest neighbor ferromagnetic vertical interaction of strength $\\gamma^{100}$ (any large power of $\\gamma$ could be handled as well) and prove that for any $\\beta$ (inverse temperature) larger than the mean field critical value there is a phase transition for all $\\gamma$ small enough.",
      "comment": "16 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-29T15:33:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B20"
    ],
    "keywords": [
      "phase transition",
      "layered systems",
      "nearest neighbor ferromagnetic vertical interaction",
      "mean field critical value",
      "two-dimensional square lattice"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Physics",
      "year": 2014,
      "month": "Nov",
      "volume": 157,
      "number": 3,
      "pages": 407
    },
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JSP...157..407F"
    }
  }
}