{
  "id": "2001.01693",
  "version": "v1",
  "published": "2020-01-06T18:04:04.000Z",
  "updated": "2020-01-06T18:04:04.000Z",
  "title": "Susceptibility of the one-dimensional Ising model: is the singularity at T = 0 an essential one?",
  "authors": [
    "James H. Taylor"
  ],
  "comment": "8 pages",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The zero-field, isothermal susceptibility of the classical one-dimensional Ising model is shown to have a relatively simple singularity as the temperature approaches zero, proportional only to the inverse temperature. This is in contrast to what is seen throughout the literature: an essential singularity involving an exponential dependence on the inverse temperature. The analysis involves nothing beyond straightforward series expansions, starting either with the partition function for a closed chain in a magnetic field, obtained using the transfer matrix approach; or from the expression for the zero-field susceptibility found via the fluctuation-dissipation theorem. In both cases, the exponential singularity is cancelled by part of a term that is usually considered ignorable in the thermodynamic limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-06T18:04:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse temperature",
      "temperature approaches zero",
      "transfer matrix approach",
      "thermodynamic limit",
      "zero-field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}