{
  "id": "2311.11721",
  "version": "v1",
  "published": "2023-11-20T12:37:34.000Z",
  "updated": "2023-11-20T12:37:34.000Z",
  "title": "When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension",
  "authors": [
    "Yulian Honchar",
    "Bertrand Berche",
    "Yurij Holovatch",
    "Ralph Kenna"
  ],
  "comment": "Submitted to Condensed Matter Physics journal",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We progress finite-size scaling in systems with free boundary conditions above their upper critical dimension, where in the thermodynamic limit critical scaling is described by mean-field theory. Recent works show that the correlation length is not bound by the system's physical size, a belief that long held sway. Instead, two scaling regimes can be observed -- at the critical and pseudo-critical temperatures. We demonstrate that both are manifest for free boundaries. We use numerical simulations of the $d=5$ Ising model to analyse the magnetization, susceptibility, magnetization Fourier modes and the partition function zeros. While some of the response functions hide the dual finite-size scaling, the precision enabled by the analysis of Lee-Yang zeros allows this be brought to the fore. In particular, finite-size scaling of leading zeros at the pseudocritical point confirms recent predictions coming from correlations exceeding system size. This paper is dedicated to Jaroslav Ilnytskyi on the occasion of his 60th birthday.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-20T12:37:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free boundary conditions",
      "upper critical dimension",
      "correlations exceed system size",
      "finite-size scaling",
      "long held sway"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}