{
  "id": "2011.05030",
  "version": "v1",
  "published": "2020-11-10T10:45:01.000Z",
  "updated": "2020-11-10T10:45:01.000Z",
  "title": "Kinetics of the Two-dimensional Long-range Ising Model at Low Temperatures",
  "authors": [
    "Ramgopal Agrawal",
    "Federico Corberi",
    "Eugenio Lippiello",
    "Paolo Politi",
    "Sanjay Puri"
  ],
  "comment": "22 pages, 12 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the low-temperature domain growth kinetics of the two-dimensional Ising model with long-range coupling: $J(r) \\sim r^{-(d+\\sigma)}$, where $d=2$ is the dimensionality. According to the Bray-Rutenberg predictions, the exponent $\\sigma$ controls the algebraic growth in time of the characteristic domain size $L(t)$, $L(t) \\sim t^{1/z}$, with growth exponent $z=1+\\sigma$ for $\\sigma <1$ and $z=2$ for $\\sigma >1$. These results hold for quenches to a non-zero temperature $T>0$ below the critical temperature $T_c$. We show that, in the case of quenches to $T=0$, due to the long-range interactions, the interfaces experience a drift which makes the dynamics of the system peculiar. More precisely we find that in this case the growth exponent takes the value $z=4/3$, independent of $\\sigma$, showing that it is a universal quantity. We support our claim by means of extended Monte Carlo simulations and analytical arguments for simplified models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-10T10:45:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-dimensional long-range ising model",
      "low temperatures",
      "growth exponent",
      "low-temperature domain growth kinetics",
      "extended monte carlo simulations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}