{
  "id": "1912.13041",
  "version": "v1",
  "published": "2019-12-30T18:17:57.000Z",
  "updated": "2019-12-30T18:17:57.000Z",
  "title": "Free Energy of the Quantum Sherrington-Kirkpatrick Spin-Glass Model with Transverse Field",
  "authors": [
    "Arka Adhikari",
    "Christian Brennecke"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the quantum Sherrington-Kirkpatrick (SK) spin-glass model with transverse field and provide a formula for its free energy in the thermodynamic limit, valid for all inverse temperatures $\\beta>0$. To characterize the free energy, we use the path integral representation of the partition function and approximate the model by a sequence of finite-dimensional vector-spin glasses with $\\mathbb{R}^d$-valued spins. This enables us to use results of Panchenko who generalized in \\cite{Pan2,Pan3} the Parisi formula to classical vector-spin glasses. As a consequence, we can express the thermodynamic limit of the free energy of the quantum SK model as the $d\\to\\infty$ limit of the free energies of the $d$-dimensional approximations of the model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-30T18:17:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free energy",
      "quantum sherrington-kirkpatrick spin-glass model",
      "transverse field",
      "thermodynamic limit",
      "quantum sk model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}