{
  "id": "cond-mat/0209674",
  "version": "v2",
  "published": "2002-09-30T11:34:10.000Z",
  "updated": "2003-02-27T17:04:10.000Z",
  "title": "Phase Transition in the ABC Model",
  "authors": [
    "M. Clincy",
    "B. Derrida",
    "M. R. Evans"
  ],
  "comment": "18 pages, 3 figures",
  "journal": "Phys. Rev. E 67, 066115 (2003)",
  "doi": "10.1103/PhysRevE.67.066115",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Recent studies have shown that one-dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules. The ABC model, which comprises three particle species that diffuse asymmetrically around a ring, shows anomalous coarsening into a phase separated steady state. In the limiting case in which the dynamics is symmetric and the parameter $q$ describing the asymmetry tends to one, no phase separation occurs and the steady state of the system is disordered. In the present work we consider the weak asymmetry regime $q=\\exp{(-\\beta/N)}$ where $N$ is the system size and study how the disordered state is approached. In the case of equal densities, we find that the system exhibits a second order phase transition at some nonzero $\\beta_c$. The value of $\\beta_c = 2 \\pi \\sqrt{3}$ and the optimal profiles can be obtained by writing the exact large deviation functional. For nonequal densities, we write down mean field equations and analyze some of their predictions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-02-27T17:04:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abc model",
      "second order phase transition",
      "exact large deviation functional",
      "weak asymmetry regime",
      "phase separation occurs"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}