{
  "id": "2112.13134",
  "version": "v3",
  "published": "2021-12-24T19:53:32.000Z",
  "updated": "2022-10-09T17:00:12.000Z",
  "title": "Cluster expansions: Necessary and sufficient convergence conditions",
  "authors": [
    "Sabine Jansen",
    "Leonid Kolesnikov"
  ],
  "journal": "J Stat Phys 189, 33 (2022)",
  "doi": "10.1007/s10955-022-02992-6",
  "categories": [
    "math-ph",
    "math.CO",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We prove a new convergence condition for the activity expansion of correlation functions in equilibrium statistical mechanics with possibly negative pair potentials. For non-negative pair potentials, the criterion is an if and only if condition. The condition is formulated with a sign-flipped Kirkwood-Salsburg operator and known conditions such as Koteck${\\'y}$-Preiss and Fern${\\'a}$ndez-Procacci are easily recovered. In addition, we deduce new sufficient convergence conditions for hard-core systems in $\\mathbb R^d$ and $\\mathbb Z^d$ as well as for abstract polymer systems. The latter improves on the Fern${\\'a}$ndez-Procacci criterion.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-10-09T17:00:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B05",
      "82B21"
    ],
    "keywords": [
      "sufficient convergence conditions",
      "cluster expansions",
      "abstract polymer systems",
      "activity expansion",
      "correlation functions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}