{
  "id": "hep-lat/9507008",
  "version": "v1",
  "published": "1995-07-07T12:26:04.000Z",
  "updated": "1995-07-07T12:26:04.000Z",
  "title": "O(N) and RP^{N-1} Models in Two Dimensions",
  "authors": [
    "Martin Hasenbusch"
  ],
  "comment": "14 pages (latex) + 1 figure (Postscript) ,uuencoded",
  "journal": "Phys.Rev. D53 (1996) 3445-3450",
  "doi": "10.1103/PhysRevD.53.3445",
  "categories": [
    "hep-lat"
  ],
  "abstract": "I provide evidence that the 2D $RP^{N-1}$ model for $N \\ge 3$ is equivalent to the $O(N)$-invariant non-linear $\\sigma$-model in the continuum limit. To this end, I mainly study particular versions of the models, to be called constraint models. I prove that the constraint $RP^{N-1}$ and $O(N)$ models are equivalent for sufficiently weak coupling. Numerical results for their step-scaling function of the running coupling $\\bar{g}^2= m(L) L$ are presented. The data confirm that the constraint $O(N)$ model is in the samei universality class as the $O(N)$ model with standard action. I show that the differences in the finite size scaling curves of $RP^{N-1}$i and $O(N)$ models observed by Caracciolo et al. can be explained as a boundary effect. It is concluded, in contrast to Caracciolo et al., that $RP^{N-1}$ and $O(N)$ models share a unique universality class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1995-07-07T12:26:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.50.+q",
      "11.15.Ha",
      "64.60.Fr",
      "11.10.Lm"
    ],
    "keywords": [
      "dimensions",
      "unique universality class",
      "samei universality class",
      "invariant non-linear",
      "continuum limit"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. D"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 397083
    }
  }
}