{
  "id": "1701.04796",
  "version": "v1",
  "published": "2017-01-17T18:21:24.000Z",
  "updated": "2017-01-17T18:21:24.000Z",
  "title": "Repulsion in low temperature $β$-ensembles",
  "authors": [
    "Yacin Ameur"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.CV",
    "math.MP"
  ],
  "abstract": "We prove a result on non-clustering of particles in a two-dimensional Coulomb plasma, which holds provided that the inverse temperature $\\beta$ satisfies $\\beta>1$. As a consequence we obtain a result on crystallization as $\\beta\\to\\infty$: the particles will, on a microscopic scale, appear at a certain distance from each other. The estimation of this distance is connected to Abrikosov's conjecture that the particles should freeze up according to a honeycomb lattice when $\\beta\\to\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-17T18:21:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "low temperature",
      "two-dimensional coulomb plasma",
      "inverse temperature",
      "microscopic scale",
      "abrikosovs conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}