{
  "id": "cond-mat/0511564",
  "version": "v1",
  "published": "2005-11-22T23:19:22.000Z",
  "updated": "2005-11-22T23:19:22.000Z",
  "title": "Directed polymers in random media under confining force",
  "authors": [
    "Hyeong-Chai Jeong"
  ],
  "comment": "9 pages, 7 figures",
  "journal": "Phys. Rev. E 72, 031803 (2005)",
  "doi": "10.1103/PhysRevE.72.031803",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The scaling behavior of a directed polymer in a two-dimensional (2D) random potential under confining force is investigated. The energy of a polymer with configuration $\\{y(x)\\}$ is given by $H\\big(\\{y(x)\\}\\big) = \\sum_{x=1}^N \\exyx + \\epsilon \\Wa^\\alpha$, where $\\eta(x,y)$ is an uncorrelated random potential and $\\Wa$ is the width of the polymer. Using an energy argument, it is conjectured that the radius of gyration $R_g(N)$ and the energy fluctuation $\\Delta E(N)$ of the polymer of length $N$ in the ground state increase as $R_g(N)\\sim N^{\\nu}$ and $\\Delta E(N)\\sim N^\\omega$ respectively with $\\nu = 1/(1+\\alpha)$ and $\\omega = (1+2\\alpha)/(4+4\\alpha)$ for $\\alpha\\ge 1/2$. A novel algorithm of finding the exact ground state, with the effective time complexity of $\\cO(N^3)$, is introduced and used to confirm the conjecture numerically.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-11-22T23:19:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "directed polymer",
      "confining force",
      "random media",
      "exact ground state",
      "ground state increase"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}