{
  "id": "2102.08073",
  "version": "v1",
  "published": "2021-02-16T10:47:55.000Z",
  "updated": "2021-02-16T10:47:55.000Z",
  "title": "On the scaling properties of (2+1) directed polymers in the high temperature limit",
  "authors": [
    "Victor Dotsenko",
    "Boris Klumov"
  ],
  "comment": "9 pages, 3 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "In this paper in terms of the replica method we consider the high temperature limit of (2+1) directed polymers in a random potential and propose an approach which allows to compute the scaling exponent $\\theta$ of the free energy fluctuations as well as the left tail of its probability distribution function. It is argued that $\\theta = 1/2$ which is different from the zero-temperature numerical value which is close to 0.241. This result implies that unlike the $(1+1)$ system in the two-dimensional case the free energy scaling exponent is non-universal being temperature dependent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-16T10:47:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high temperature limit",
      "directed polymers",
      "scaling properties",
      "free energy fluctuations",
      "probability distribution function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}