{
  "id": "1403.1836",
  "version": "v3",
  "published": "2014-03-07T18:57:57.000Z",
  "updated": "2014-10-20T18:05:51.000Z",
  "title": "Correlation function for the Grid-Poisson Euclidean matching on a line and on a circle",
  "authors": [
    "Elena Boniolo",
    "Sergio Caracciolo",
    "Andrea Sportiello"
  ],
  "comment": "34 pages, 10 figures",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "We compute the two-point correlation function for spin configurations which are obtained by solving the Euclidean matching problem, for one family of points on a grid, and the second family chosen uniformly at random, when the cost depends on a power $p$ of the Euclidean distance. We provide the analytic solution in the thermodynamic limit, in a number of cases ($p>1$ open b.c.\\ and $p=2$ periodic b.c., both at criticality), and analyse numerically other parts of the phase diagram.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-04T15:14:55.000Z",
      "abstract": "We compute the two-point correlation function for spin configurations which are obtained by solving the matching problem of points on grid with points chosen at random when the cost depends on their distance. We provide the analytical solution in the continuum in some particular case and check it numerically by looking at the critical problem on the finite size.",
      "comment": "29 pages, 10 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-10-20T18:05:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grid-poisson euclidean matching",
      "two-point correlation function",
      "spin configurations",
      "points chosen",
      "cost depends"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1742-5468/2014/11/P11023",
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2014,
      "month": "Nov",
      "volume": 2014,
      "number": 11,
      "pages": 11023
    },
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JSMTE..11..023B"
    }
  }
}