{
  "id": "cond-mat/0001277",
  "version": "v1",
  "published": "2000-01-19T17:37:57.000Z",
  "updated": "2000-01-19T17:37:57.000Z",
  "title": "Phase Transition in the Takayasu Model with Desorption",
  "authors": [
    "Satya N. Majumdar",
    "Supriya Krishnamurthy",
    "Mustansir Barma"
  ],
  "comment": "RevTex, 11 pages including 5 figures, submitted to Phys. Rev. E",
  "doi": "10.1103/PhysRevE.61.6337",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study a lattice model where particles carrying different masses diffuse, coalesce upon contact, and also unit masses adsorb to a site with rate $q$ or desorb from a site with nonzero mass with rate $p$. In the limit $p=0$ (without desorption), our model reduces to the well studied Takayasu model where the steady-state single site mass distribution has a power law tail $P(m)\\sim m^{-\\tau}$ for large mass. We show that varying the desorption rate $p$ induces a nonequilibrium phase transition in all dimensions. For fixed $q$, there is a critical $p_c(q)$ such that if $p<p_c(q)$, the steady state mass distribution, $P(m)\\sim m^{-\\tau}$ for large $m$ as in the Takayasu case. For $p=p_c(q)$, we find $P(m)\\sim m^{-\\tau_c}$ where $\\tau_c$ is a new exponent, while for $p>p_c(q)$, $P(m)\\sim \\exp(-m/m^*)$ for large $m$. The model is studied analytically within a mean field theory and numerically in one dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-01-19T17:37:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "takayasu model",
      "desorption",
      "steady-state single site mass distribution",
      "steady state mass distribution",
      "power law tail"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}