{
  "id": "1008.2037",
  "version": "v1",
  "published": "2010-08-12T03:50:09.000Z",
  "updated": "2010-08-12T03:50:09.000Z",
  "title": "Coherent potential approximation of random nearly isostatic kagome lattice",
  "authors": [
    "Xiaoming Mao",
    "T. C. Lubensky"
  ],
  "comment": "15 pages, 8 figures",
  "journal": "Physical Review E 83, 011111 (2011)",
  "doi": "10.1103/PhysRevE.83.011111",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.soft",
    "cond-mat.stat-mech"
  ],
  "abstract": "The kagome lattice has coordination number $4$, and it is mechanically isostatic when nearest neighbor ($NN$) sites are connected by central force springs. A lattice of $N$ sites has $O(\\sqrt{N})$ zero-frequency floppy modes that convert to finite-frequency anomalous modes when next-nearest-neighbor ($NNN$) springs are added. We use the coherent potential approximation (CPA) to study the mode structure and mechanical properties of the kagome lattice in which $NNN$ springs with spring constant $\\kappa$ are added with probability $\\Prob= \\Delta z/4$, where $\\Delta z= z-4$ and $z$ is the average coordination number. The effective medium static $NNN$ spring constant $\\kappa_m$ scales as $\\Prob^2$ for $\\Prob \\ll \\kappa$ and as $\\Prob$ for $\\Prob \\gg \\kappa$, yielding a frequency scale $\\omega^* \\sim \\Delta z$ and a length scale $l^*\\sim (\\Delta z)^{-1}$. To a very good approximation at at small nonzero frequency, $\\kappa_m(\\Prob,\\omega)/\\kappa_m(\\Prob,0)$ is a scaling function of $\\omega/\\omega^*$. The Ioffe-Regel limit beyond which plane-wave states becomes ill-define is reached at a frequency of order $\\omega^*$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-12T03:50:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46.65.+g",
      "05.70.Jk",
      "61.43.-j",
      "62.20.de"
    ],
    "keywords": [
      "coherent potential approximation",
      "isostatic kagome lattice",
      "average coordination number",
      "spring constant",
      "central force springs"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2011,
      "month": "Jan",
      "volume": 83,
      "number": 1,
      "pages": "011111"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhRvE..83a1111M"
    }
  }
}