{
  "id": "math-ph/0103002",
  "version": "v1",
  "published": "2001-03-03T02:17:42.000Z",
  "updated": "2001-03-03T02:17:42.000Z",
  "title": "Geometric and probabilistic aspects of boson lattice models",
  "authors": [
    "D. Ueltschi"
  ],
  "comment": "22 pages, 8 figures",
  "journal": "Progr. Probab. 51, 363-391, Birkh\\\"auser (2002)",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "This review describes quantum systems of bosonic particles moving on a lattice. These models are relevant in statistical physics, and have natural ties with probability theory. The general setting is recalled and the main questions about phase transitions are addressed. A lattice model with Lennard-Jones potential is studied as an example of a system where first-order phase transitions occur. A major interest of bosonic systems is the possibility of displaying a Bose-Einstein condensation. This is discussed in the light of the main existing rigorous result, namely its occurrence in the hard-core boson model. Finally, we consider another approach that involves the lengths of the cycles formed by the particles in the space-time representation; Bose-Einstein condensation should be related to positive probability of infinite cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-03-03T02:17:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B10",
      "82B20",
      "82B26",
      "82B41",
      "60K40"
    ],
    "keywords": [
      "boson lattice models",
      "probabilistic aspects",
      "bose-einstein condensation",
      "first-order phase transitions occur",
      "hard-core boson model"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.ph...3002U"
    }
  }
}