{
  "id": "2006.13061",
  "version": "v1",
  "published": "2020-06-23T14:36:21.000Z",
  "updated": "2020-06-23T14:36:21.000Z",
  "title": "Asymptotic low-temperature behavior of two-dimensional RP$^{N-1}$ models",
  "authors": [
    "Claudio Bonati",
    "Alessio Franchi",
    "Andrea Pelissetto",
    "Ettore Vicari"
  ],
  "comment": "10 pages, 9 eps figures",
  "categories": [
    "cond-mat.stat-mech",
    "hep-lat"
  ],
  "abstract": "We investigate the low-temperature behavior of two-dimensional (2D) RP$^{N-1}$ models, characterized by a global O($N$) symmetry and a local ${\\mathbb Z}_2$ symmetry. For $N=3$ we perform large-scale simulations of four different 2D lattice models: two standard lattice models and two different constrained models. We also consider a constrained mixed O(3)-RP$^2$ model for values of the parameters such that vector correlations are always disordered. We find that all these models show the same finite-size scaling (FSS) behavior, and therefore belong to the same universality class. However, these FSS curves differ from those computed in the 2D O(3) $\\sigma$ model, suggesting the existence of a distinct 2D RP$^2$ universality class. We also performed simulations for $N=4$, and the corresponding FSS results also support the existence of an RP$^3$ universality class, different from the O(4) one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-23T14:36:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic low-temperature behavior",
      "two-dimensional rp",
      "universality class",
      "2d lattice models",
      "standard lattice models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}