{
  "id": "1902.07099",
  "version": "v1",
  "published": "2019-02-19T15:33:35.000Z",
  "updated": "2019-02-19T15:33:35.000Z",
  "title": "Why replica symmetry breaking does not occur below six dimensions in Ising spin glasses",
  "authors": [
    "M. A. Moore"
  ],
  "comment": "5 pages, one figure",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "The leading term for the average height of the barriers which could separate pure states in Ising spin glasses is calculated using instanton methods. It is finite in dimensions $d < 6$. Replica symmetry breaking requires that the barriers between pure states are infinite in the thermodynamic limit, as finite barriers allow thermal mixing of pure states. As a consequence, a replica symmetry broken phase cannot survive when $d < 6$. However, for $d > 6$ no similar instanton solution exists.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-19T15:33:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ising spin glasses",
      "replica symmetry breaking",
      "dimensions",
      "replica symmetry broken phase",
      "separate pure states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}