{
  "id": "2505.06209",
  "version": "v1",
  "published": "2025-05-09T17:39:58.000Z",
  "updated": "2025-05-09T17:39:58.000Z",
  "title": "Random currents for signed interactions in the one-dimensional heterogeneous Ising model",
  "authors": [
    "Edward Athaide",
    "Maciej Głuchowski",
    "Jonas Köppl",
    "Georg Menz"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The random current representation has been very successful in analyzing the ferromagnetic Ising model. In this article, we extend the method to the non-ferromagnetic case. To show its usefulness, we derive a covariance identity for the heterogeneous one-dimensional Ising model, which recovers the correct rate of exponential decay of covariances in the case of random i.i.d. interaction and external field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-09T17:39:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B20",
      "60K35"
    ],
    "keywords": [
      "one-dimensional heterogeneous ising model",
      "signed interactions",
      "random current representation",
      "heterogeneous one-dimensional ising model",
      "non-ferromagnetic case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}