{
  "id": "cond-mat/0607423",
  "version": "v3",
  "published": "2006-07-17T14:48:45.000Z",
  "updated": "2006-08-25T10:17:28.000Z",
  "title": "High-temperature series expansions for the $q$-state Potts model on a hypercubic lattice and critical properties of percolation",
  "authors": [
    "Meik Hellmund",
    "Wolfhard Janke"
  ],
  "comment": "2 references added",
  "journal": "Phys. Rev. E74(2006)051113",
  "doi": "10.1103/PhysRevE.74.051113",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We present results for the high-temperature series expansions of the susceptibility and free energy of the $q$-state Potts model on a $D$-dimensional hypercubic lattice $\\mathbb{Z}^D$ for arbitrary values of $q$. The series are up to order 20 for dimension $D\\leq3$, order 19 for $D\\leq 5$ and up to order 17 for arbitrary $D$. Using the $q\\to 1$ limit of these series, we estimate the percolation threshold $p_c$ and critical exponent $\\gamma$ for bond percolation in different dimensions. We also extend the 1/D expansion of the critical coupling for arbitrary values of $q$ up to order $D^{-9}$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-08-25T10:17:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "state potts model",
      "high-temperature series expansions",
      "critical properties",
      "percolation",
      "arbitrary values"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}