{
  "id": "cond-mat/0502062",
  "version": "v2",
  "published": "2005-02-02T16:25:46.000Z",
  "updated": "2005-09-26T11:03:58.000Z",
  "title": "Fractal Structure of High-Temperature Graphs of O($N$) Models in Two Dimensions",
  "authors": [
    "Wolfhard Janke",
    "Adriaan M. J. Schakel"
  ],
  "comment": "4 pages, no figures; 2nd version: Introduction rewritten, comparison of prediction with recent high-precision Monte Carlo data with figure included, references added",
  "journal": "Phys. Rev. Lett. 95, 135702 (2005)",
  "doi": "10.1103/PhysRevLett.95.135702",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The fractal structure and critical properties of the high-temperature graphs of the two-dimensional O($N)$ model close to criticality are investigated. Based on Monte Carlo simulations, De Gennes' results for polymer chains, corresponding to the limit $N \\to 0$, are generalized to random loops for arbitrary $-2 \\leq N \\leq 2$. The loops are also studied close to their tricritical point, known as the $\\Theta$ point in the context of polymers, where they collapse. The corresponding fractal dimensions are argued to be in one-to-one correspondence with those at the critical point, leading to an analytic prediction for the magnetic scaling dimension at the O($N)$ tricritical point.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-09-26T11:03:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractal structure",
      "high-temperature graphs",
      "monte carlo simulations",
      "tricritical point",
      "polymer chains"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}