{
  "id": "1411.6802",
  "version": "v1",
  "published": "2014-11-25T10:39:22.000Z",
  "updated": "2014-11-25T10:39:22.000Z",
  "title": "Metastability of the Ising model on random regular graphs at zero temperature",
  "authors": [
    "Sander Dommers"
  ],
  "categories": [
    "math.PR",
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the metastability of the ferromagnetic Ising model on a random $r$-regular graph in the zero temperature limit. We prove that in the presence of a small positive external field the time that it takes to go from the all minus state to the all plus state behaves like ${\\exp(\\beta (r/2+ \\mathcal{O}(\\sqrt{r}))n)}$ when the inverse temperature $\\beta\\rightarrow\\infty$ and the number of vertices $n$ is large enough. The proof is based on the so-called pathwise approach and bounds on the isoperimetric number of random regular graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-25T10:39:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C20"
    ],
    "keywords": [
      "random regular graphs",
      "metastability",
      "zero temperature limit",
      "plus state behaves",
      "small positive external field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.6802D"
    }
  }
}