{
  "id": "1511.02790",
  "version": "v1",
  "published": "2015-11-09T18:11:58.000Z",
  "updated": "2015-11-09T18:11:58.000Z",
  "title": "Finite-order correlation length for 4-dimensional weakly self-avoiding walk and $|\\varphi|^4$ spins",
  "authors": [
    "Roland Bauerschmidt",
    "Gordon Slade",
    "Alexandre Tomberg",
    "Benjamin C. Wallace"
  ],
  "comment": "22 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We study the 4-dimensional $n$-component $|\\varphi|^4$ spin model for all integers $n \\ge 1$, and the 4-dimensional continuous-time weakly self-avoiding walk which corresponds exactly to the case $n=0$ interpreted as a supersymmetric spin model. For these models, we analyse the correlation length of order $p$, and prove the existence of a logarithmic correction to mean-field scaling, with power $\\frac 12\\frac{n+2}{n+8}$, for all $n \\ge 0$ and $p>0$. The proof is based on an improvement of a rigorous renormalisation group method developed previously.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-09T18:11:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B27",
      "82B28",
      "60K35",
      "82B41"
    ],
    "keywords": [
      "finite-order correlation length",
      "rigorous renormalisation group method",
      "supersymmetric spin model",
      "continuous-time weakly self-avoiding walk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1403632
    }
  }
}