2012/07/02 by Jørgen Rasmussen, Jorgen Rasmussen, Philippe Ruelle · 14 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Central charge #Combinatorics #Computer science #Conformal field theory #Conformal map #Conformal symmetry #Dimer #Disjoint sets #Geometry #Integer (computer science) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Primary field #Pure mathematics #Scaling #Scaling limit #Theoretical and Computational Physics #Transfer matrix #cond-mat.stat-mech #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1742-5468/2012/10/p10002
published in Journal of Statistical Mechanics Theory and Experiment 2012(10), P10002 (Institute of Physics) · 44 pages
arxiv created 2012/07/02 · openalex publication_date 2012/10/04 · arxiv updated 2015/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Working with Lieb's transfer matrix for the dimer model, we point out that the full set of dimer configurations may be partitioned into disjoint subsets (sectors) closed under the action of the transfer matrix. These sectors are labelled by an integer or half-integer quantum number we call the variation index. In the continuum scaling limit, each sector gives rise to a representation of the Virasoro algebra. We determine the corresponding conformal partition functions and their finitizations, and observe an intriguing link to the Ramond and Neveu–Schwarz sectors of the critical dense polymer model as described by a conformal field theory with central charge c =− 2.