{
  "id": "1906.11980",
  "version": "v1",
  "published": "2019-06-27T22:03:02.000Z",
  "updated": "2019-06-27T22:03:02.000Z",
  "title": "The log-Sobolev inequality for spin systems of higher order interactions",
  "authors": [
    "Takis Konstantopoulos",
    "Ioannis Papageorgiou"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We study the infinite-dimensional log-Sobolev inequality for spin systems on $\\mathbb{Z}^d$ with interactions of power higher than quadratic. We assume that the one site measure without a boundary $e^{-\\phi(x)}dx/Z$ satisfies a log-Sobolev inequality and we determine conditions so that the infinite-dimensional Gibbs measure also satisfies the inequality. As a concrete application, we prove that a certain class of nontrivial Gibbs measures with non-quadratic interaction potentials on an infinite product of Heisenberg groups satisfy the log-Sobolev inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-27T22:03:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "26D10",
      "39B62",
      "22E30"
    ],
    "keywords": [
      "higher order interactions",
      "spin systems",
      "non-quadratic interaction potentials",
      "infinite-dimensional log-sobolev inequality",
      "nontrivial gibbs measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}