{
  "id": "0911.2096",
  "version": "v3",
  "published": "2009-11-11T10:06:34.000Z",
  "updated": "2010-04-14T08:48:13.000Z",
  "title": "Mapping all classical spin models to a lattice gauge theory",
  "authors": [
    "G. De las Cuevas",
    "W. Dür",
    "H. J. Briegel",
    "M. A. Martin-Delgado"
  ],
  "comment": "21 pages, 21 figures; published version",
  "journal": "New J. Phys. 12, 043014 (2010)",
  "doi": "10.1088/1367-2630/12/4/043014",
  "categories": [
    "quant-ph",
    "cond-mat.stat-mech",
    "hep-lat"
  ],
  "abstract": "In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), can be expressed as a special instance of the partition function of a 4-dimensional pure LGT with gauge group Z_2 (4D Z_2 LGT). This provides a unification of models with apparently very different features into a single complete model. The result uses an equality between the Hamilton function of any classical spin model and the Hamilton function of a model with all possible k-body Ising-type interactions, for all k, which we also prove. Here, we elaborate on the proof of the result, and we illustrate it by computing quantities of a specific model as a function of the partition function of the 4D Z_2 LGT. The result also allows one to establish a new method to compute the mean-field theory of Z_2 LGTs with d > 3, and to show that computing the partition function of the 4D Z_2 LGT is computationally hard (#P hard). The proof uses techniques from quantum information.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-04-14T08:48:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.67.Lx",
      "05.50.+q",
      "03.67.-a",
      "11.15.Ha",
      "75.10.Hk"
    ],
    "keywords": [
      "lattice gauge theory",
      "classical spin model",
      "partition function",
      "abelian discrete lattice gauge theories",
      "hamilton function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "New Journal of Physics",
      "year": 2010,
      "month": "Apr",
      "volume": 12,
      "number": 4,
      "pages": "043014"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 836804,
      "adsabs": "2010NJPh...12d3014D"
    }
  }
}