2015/09/30 by Eric Vernier, Éric Vernier, Jesper Lykke Jacobsen +1
Materials Science · Mathematics · Physics and Astronomy · #Combinatorics #Condensed matter physics #Conformal field theory #Conformal map #Geometry #Hexagonal lattice #Lattice (music) #Liquid Crystal Research Advancements #Mathematical physics #Mathematics #Photonic Crystals and Applications #Physics #Quasicrystal Structures and Properties #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/49/17/174004
published as J. Phys. A: Math. Theor. 49 (2016) 174004 [45 pages] · 51 pages (pdflatex). Contains a .bbl file, and 9 figures in pdf format. The tex source uses IOP and tikz macros (not included). v2 contains many changes with respect to v1. Final version published in journal
openalex publication_date 2016/03/18 · arxiv created 2016/04/05 · arxiv updated 2016/04/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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 , where . 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 . 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.