{
  "id": "1602.04048",
  "version": "v1",
  "published": "2016-02-12T13:28:58.000Z",
  "updated": "2016-02-12T13:28:58.000Z",
  "title": "Renormalisation group analysis of 4D spin models and self-avoiding walk",
  "authors": [
    "Roland Bauerschmidt",
    "David C. Brydges",
    "Gordon Slade"
  ],
  "comment": "Proceedings for ICMP, Santiago de Chile, July 2015",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We give an overview of results on critical phenomena in 4 dimensions, obtained recently using a rigorous renormalisation group method. In particular, for the $n$-component $|\\varphi|^4$ spin model in dimension 4, with small coupling constant, we prove that the susceptibility diverges with a logarithmic correction to the mean-field behaviour with exponent $(n+2)/(n+8)$. This result extends rigorously to $n=0$, interpreted as a supersymmetric version of the model that represents exactly the continuous-time weakly self-avoiding walk. We also analyse the critical two-point function of the weakly self-avoiding walk, the specific heat and pressure of the $|\\varphi|^4$ model, as well as scaling limits of the spin field close to the critical point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-12T13:28:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B27",
      "82B28",
      "60K35",
      "82B41"
    ],
    "keywords": [
      "4d spin models",
      "renormalisation group analysis",
      "weakly self-avoiding walk",
      "spin field close",
      "rigorous renormalisation group method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160204048B",
      "inspire": 1421882
    }
  }
}