{
  "id": "1802.07151",
  "version": "v1",
  "published": "2018-02-20T15:30:00.000Z",
  "updated": "2018-02-20T15:30:00.000Z",
  "title": "Exact results for the $O(N)$ model with quenched disorder",
  "authors": [
    "Gesualdo Delfino",
    "Noel Lamsen"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "hep-th"
  ],
  "abstract": "We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points for $O(N)$-symmetric models with quenched disorder in two dimensions. Random fixed points are characterized by two disorder parameters: a modulus that vanishes when approaching the pure case, and a phase angle. The critical lines fall into three classes depending on the values of the disorder modulus. Besides the class corresponding to the pure case, a second class has maximal value of the disorder modulus and includes Nishimori-like multicritical points as well as zero temperature fixed points. The third class contains critical lines that interpolate, as $N$ varies, between the first two classes. For positive $N$, it contains a single line of infrared fixed points spanning the values of $N$ from $\\sqrt{2}-1$ to $1$. The symmetry sector of the energy density operator is superuniversal (i.e. $N$-independent) along this line. For $N=2$ a line of fixed points exists only in the pure case, but accounts also for the Berezinskii-Kosterlitz-Thouless phase observed in presence of disorder.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-20T15:30:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quenched disorder",
      "exact results",
      "pure case",
      "disorder modulus",
      "third class contains critical lines"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}