{
  "id": "2011.09802",
  "version": "v1",
  "published": "2020-11-19T13:00:49.000Z",
  "updated": "2020-11-19T13:00:49.000Z",
  "title": "Non-analyticity of the correlation length in systems with exponentially decaying interactions",
  "authors": [
    "Yacine Aoun",
    "Dmitry Ioffe",
    "Sébastien Ott",
    "Yvan Velenik"
  ],
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a variety of lattice spin systems (including Ising, Potts and XY models) on $\\mathbb{Z}^d$ with long-range interactions of the form $J_x = \\psi(x) e^{-|x|}$, where $\\psi(x) = e^{\\mathsf{o}(|x|)}$ and $|\\cdot|$ is an arbitrary norm. We characterize explicitly the prefactors $\\psi$ that give rise to a correlation length that is not analytic in the relevant external parameter(s) (inverse temperature $\\beta$, magnetic field $h$, etc). Our results apply in any dimension. As an interesting particular case, we prove that, in one-dimensional systems, the correlation length is non-analytic whenever $\\psi$ is summable, in sharp contrast to the well-known analytic behavior of all standard thermodynamic quantities. We also point out that this non-analyticity, when present, also manifests itself in a qualitative change of behavior of the 2-point function. In particular, we relate the lack of analyticity of the correlation length to the failure of the mass gap condition in the Ornstein--Zernike theory of correlations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-19T13:00:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "correlation length",
      "exponentially decaying interactions",
      "non-analyticity",
      "lattice spin systems",
      "mass gap condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}