{
  "id": "2406.06249",
  "version": "v1",
  "published": "2024-06-10T13:26:08.000Z",
  "updated": "2024-06-10T13:26:08.000Z",
  "title": "Hierarchical Cubes: Gibbs Measures and Decay of Correlations",
  "authors": [
    "Sabine Jansen",
    "Jan Philipp Neumann"
  ],
  "comment": "28 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We study a hierarchical model of non-overlapping cubes of sidelengths $2^j$, $j \\in \\mathbb{Z}$. The model allows for cubes of arbitrarily small size and the activities need not be translationally invariant. It can also be recast as a spin system on a tree with long-range hard-core interaction. We prove necessary and sufficient conditions for the existence and uniqueness of Gibbs measures, discuss fragmentation and condensation, and prove bounds on the decay of two-point correlation functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-10T13:26:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B20"
    ],
    "keywords": [
      "gibbs measures",
      "hierarchical cubes",
      "two-point correlation functions",
      "long-range hard-core interaction",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}