{
  "id": "1810.13138",
  "version": "v1",
  "published": "2018-10-31T07:48:30.000Z",
  "updated": "2018-10-31T07:48:30.000Z",
  "title": "Critical exponent for the magnetization of the weakly coupled $φ^4_4$ model",
  "authors": [
    "Martin Lohmann"
  ],
  "comment": "49 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the weakly coupled $\\phi^4 $ theory on $\\mathbb Z^4 $, in a weak magnetic field $h$, and at the chemical potential $\\nu_c $ for which the theory is critical if $h=0$. We prove that, as $h\\to 0$, the magnetization of the model behaves as $(h\\log h^{-1})^{\\frac 13} $, and so exhibits a logarithmic correction to mean field scaling behavior. This result is well known to physicists, but had never been proven rigorously. Our proof uses the classic construction of the critical theory by Gawedzki and Kupiainen, and a cluster expansion with large blocks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-31T07:48:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical exponent",
      "magnetization",
      "weak magnetic field",
      "mean field scaling behavior",
      "logarithmic correction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}