{
  "id": "2103.08695",
  "version": "v1",
  "published": "2021-03-15T20:23:16.000Z",
  "updated": "2021-03-15T20:23:16.000Z",
  "title": "Boundary effects on finite-size scaling for the 5-dimensional Ising model",
  "authors": [
    "P. H. Lundow"
  ],
  "comment": "7 pages, 16 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "High-dimensional ($d\\ge 5$) Ising systems have mean-field critical exponents. However, at the critical temperature the finite-size scaling of the susceptibility $\\chi$ depends on the boundary conditions. A system with periodic boundary conditions then has $\\chi\\propto L^{5/2}$. Deleting the $5L^4$ boundary edges we receive a system with free boundary conditions and now $\\chi\\propto L^2$. In the present work we find that deleting the $L^4$ boundary edges along just one direction is enough to have the scaling $\\chi\\propto L^2$. It also appears that deleting $L^3$ boundary edges results in an intermediate scaling, here estimated to $\\chi\\propto L^{2.275}$. We also study how the energy and magnetisation distributions change when deleting boundary edges.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-15T20:23:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boundary effects",
      "finite-size scaling",
      "ising model",
      "boundary edges results",
      "free boundary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}