{
  "id": "0912.1251",
  "version": "v1",
  "published": "2009-12-07T14:32:09.000Z",
  "updated": "2009-12-07T14:32:09.000Z",
  "title": "On Spin Systems with Quenched Randomness: Classical and Quantum",
  "authors": [
    "Rafael L Greenblatt",
    "Michael Aizenman",
    "Joel L. Lebowitz"
  ],
  "comment": "8 pages LaTeX, 2 PDF figures. Presented by JLL at the symposium \"Trajectories and Friends\" in honor of Nihat Berker, MIT, October 2009",
  "journal": "Physica A (2010) 389: 2902-2906",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "The rounding of first order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a $d$-dimensional lattice is continuously differentiable with respect to any parameter in the Hamiltonian to which some randomness has been added when $d \\leq 2$. This implies absence of jumps in the associated order parameter, e.g., the magnetization in case of a random magnetic field. A similar result applies in cases of continuous symmetry breaking for $d \\leq 4$. Some questions concerning the behavior of related order parameters in such random systems are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-07T14:32:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spin system",
      "quenched randomness",
      "first order phase transitions",
      "order parameter",
      "similar result applies"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.physa.2009.12.066",
      "journal": "Physica A Statistical Mechanics and its Applications",
      "year": 2010,
      "month": "Aug",
      "volume": 389,
      "number": 15,
      "pages": 2902
    },
    "note": {
      "typesetting": "PDFLaTeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010PhyA..389.2902G"
    }
  }
}