{
  "id": "1211.1462",
  "version": "v1",
  "published": "2012-11-07T06:36:39.000Z",
  "updated": "2012-11-07T06:36:39.000Z",
  "title": "Coarsening of two dimensional XY model with Hamiltonian dynamics: Logarithmically divergent vortex mobility",
  "authors": [
    "Keekwon Nam",
    "Woon-Bo Baek",
    "Bongsoo Kim",
    "Sung Jong Lee"
  ],
  "comment": "11 pages, 10 figures. arXiv admin note: text overlap with arXiv:cond-mat/0610590",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We investigate the coarsening kinetics of an XY model defined on a square lattice when the underlying dynamics is governed by energy-conserving Hamiltonian equation of motion. We find that the apparent super-diffusive growth of the length scale can be interpreted as the vortex mobility diverging logarithmically in the size of the vortex-antivortex pair, where the time dependence of the characteristic length scale can be fitted as $L(t) \\sim ((t+t_{0}) \\ln(t+t_{0}))^{1/2}$ with a finite offset time $t_0$. This interpretation is based on a simple phenomenological model of vortex-antivortex annihilation to explain the growth of the coarsening length scale $L(t)$. The nonequilibrium spin autocorrelation function $A(t)$ and the growing length scale $L(t)$ are related by $A(t) \\simeq L^{-\\lambda}(t)$ with a distinctive exponent of $\\lambda \\simeq 2.21$ (for $E=0.4$) possibly reflecting the strong effect of propagating spin wave modes. We also investigate the nonequilibrium relaxation (NER) of the system under sudden heating of the system from a perfectly ordered state to the regime of quasi-long-range order, which provides a very accurate estimation of the equilibrium correlation exponent $\\eta (E) $ for a given energy $E$. We find that both the equal-time spatial correlation $C_{nr}(r,t)$ and the NER autocorrelation $A_{nr}(t)$ exhibit scaling features consistent with the dynamic exponent of $z_{nr} = 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-07T06:36:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "logarithmically divergent vortex mobility",
      "dimensional xy model",
      "hamiltonian dynamics",
      "nonequilibrium spin autocorrelation function",
      "coarsening"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1742-5468/2012/11/P11023",
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2012,
      "month": "Nov",
      "volume": 2012,
      "number": 11,
      "pages": 11023
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JSMTE..11..023N"
    }
  }
}