{
  "id": "2410.20610",
  "version": "v1",
  "published": "2024-10-27T21:58:52.000Z",
  "updated": "2024-10-27T21:58:52.000Z",
  "title": "Critical Droplets and Replica Symmetry Breaking",
  "authors": [
    "C. M. Newman",
    "D. L. Stein"
  ],
  "comment": "12 pages, no figures",
  "categories": [
    "cond-mat.dis-nn",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show that the notion of critical droplets is central to an understanding of the nature of ground states in the Edwards-Anderson Ising model of a spin glass in arbitrary dimension. Given a specific ground state, suppose the coupling value for a given edge is varied with all other couplings held fixed. Beyond some specific value of the coupling, a droplet will flip leading to a new ground state; we refer to this as the critical droplet for that edge and ground state. We show that the distribution of sizes and energies over all edges for a specific ground state can be used to determine which of the leading scenarios for the spin glass phase is correct. In particular, the existence of low-energy interfaces between incongruent ground states as predicted by replica symmetry breaking is equivalent to the presence of critical droplets whose boundaries comprise a positive fraction of edges in the infinite lattice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-27T21:58:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "replica symmetry breaking",
      "critical droplet",
      "specific ground state",
      "spin glass phase",
      "incongruent ground states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}