{
  "id": "1711.09652",
  "version": "v1",
  "published": "2017-11-27T12:36:51.000Z",
  "updated": "2017-11-27T12:36:51.000Z",
  "title": "Growing interfaces: A brief review on the tilt method",
  "authors": [
    "M. F. Torres",
    "R. C. Buceta"
  ],
  "comment": "11 pages, 4 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The tilt method applied to models of growing interfaces is a useful tool to characterize the nonlinearities of their associated equation. Growing interfaces with average slope $m$, in models and equations belonging to Kardar-Parisi-Zhang (KPZ) universality class, have average saturation velocity $\\mathcal{V}_\\mathrm{sat}=\\Upsilon+\\frac{1}{2}\\Lambda\\,m^2$ when $|m|\\ll 1$. This property is sufficient to ensure that there is a nonlinearity type square height-gradient. Usually, the constant $\\Lambda$ is considered equal to the nonlinear coefficient $\\lambda$ of the KPZ equation. In this paper, we show that the mean square height-gradient $\\langle |\\nabla h|^2\\rangle=a+b \\,m^2$, where $b=1$ for the continuous KPZ equation and $b\\neq 1$ otherwise, e.g. ballistic deposition (BD) and restricted-solid-on-solid (RSOS) models. In order to find the nonlinear coefficient $\\lambda$ associated to each system, we establish the relationship $\\Lambda=b\\,\\lambda$ and we test it through the discrete integration of the KPZ equation. We conclude that height-gradient fluctuations as function of $m^2$ are constant for continuous KPZ equation and increasing or decreasing in other systems, such as BD or RSOS models, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-27T12:36:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "growing interfaces",
      "tilt method",
      "brief review",
      "continuous kpz equation",
      "nonlinear coefficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}