{
  "id": "hep-th/9304078",
  "version": "v2",
  "published": "1993-04-19T16:26:34.000Z",
  "updated": "1993-04-26T21:40:03.000Z",
  "title": "Violations of the String Hypothesis in the Solutions of the Bethe Ansatz Equations in the XXX-Heisenberg",
  "authors": [
    "K. Isler",
    "M. B. Paranjape"
  ],
  "comment": "18 pages. revised to amplify credit, in plain tex with macropackage psbox (available from the net)",
  "journal": "Phys.Lett. B319 (1993) 209-214",
  "doi": "10.1016/0370-2693(93)90804-Q",
  "categories": [
    "hep-th"
  ],
  "abstract": "We study the equations for the quasi-momenta which characterize the wave-functions in the Bethe ansatz for the XXX-Heisenberg model. We show in a simple analytical fashion, that the usual ``string hypothesis\" incorrectly predicts the number of real solutions and the number of complex solutions for $N>21$ in the sector with two spins flipped, confirming the work of Essler et al. Two complex pair solutions drop out and form two additional real pair solutions. We also introduce a new set of variables which allows the equations to be written as a single polynomial equation in one variable. We consider in some detail the case of three spins flipped.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1993-04-26T21:40:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bethe ansatz equations",
      "string hypothesis",
      "xxx-heisenberg",
      "additional real pair solutions",
      "complex pair solutions drop"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 35267
    }
  }
}