{
  "id": "1509.02804",
  "version": "v1",
  "published": "2015-09-09T15:13:19.000Z",
  "updated": "2015-09-09T15:13:19.000Z",
  "title": "Q-colourings of the triangular lattice: Exact exponents and conformal field theory",
  "authors": [
    "Eric Vernier",
    "Jesper Lykke Jacobsen",
    "Jesús Salas"
  ],
  "comment": "40 pages (pdflatex). Contains a .bib file, the corresponding .bbl file, and 8 figures in pdf format. The tex source uses IOP and tikz macros (not included)",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We revisit the problem of Q-colourings of the triangular lattice using a mapping onto an integrable spin-one model, which can be solved exactly using Bethe Ansatz techniques. In particular we focus on the low-energy excitations above the eigenlevel g_2, which was shown by Baxter to dominate the transfer matrix spectrum in the Fortuin-Kasteleyn (chromatic polynomial) representation for Q_0 <= Q <= 4, where Q_0 = 3.819671... We argue that g_2 and its scaling levels define a conformally invariant theory, the so-called regime IV, which provides the actual description of the (analytically continued) colouring problem within a much wider range, namely 2 < Q <= 4. The corresponding conformal field theory is identified and the exact critical exponents are derived. We discuss their implications for the phase diagram of the antiferromagnetic triangular-lattice Potts model at non-zero temperature. Finally, we relate our results to recent observations in the field of spin-one anyonic chains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-09T15:13:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "triangular lattice",
      "exact exponents",
      "q-colourings",
      "antiferromagnetic triangular-lattice potts model",
      "transfer matrix spectrum"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/49/17/174004",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2016,
      "month": "Apr",
      "volume": 49,
      "number": 17,
      "pages": 174004
    },
    "note": {
      "typesetting": "PDFLaTeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016JPhA...49q4004V",
      "inspire": 1392704
    }
  }
}