2013/07/31 by Gesualdo Delfino, G Delfino, Marco Picco +5 · 7 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Conformal field theory #Conformal map #Field (mathematics) #Physics of Superconductivity and Magnetism #Quantum many-body systems #Spin (aerodynamics) #Spin glass #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1088/1742-5468/2013/11/p11011
published in Journal of Statistical Mechanics Theory and Experiment 2013(11), P11011 (Institute of Physics) · 16 pages, 8 Figures, Revised version (Fig. 7 added)
arxiv created 2013/10/11 · openalex publication_date 2013/11/27 · arxiv updated 2014/10/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We study numerically the fractal dimensions and the bulk three-point connectivity for spin clusters of the Q -state Potts model in two dimensions with 1 ≤ Q ≤ 4. We check that the usually invoked correspondence between FK clusters and spin clusters works at the level of fractal dimensions. However, the fine structure of the conformal field theories describing critical clusters first manifests at the level of the three-point connectivities. Contrary to what was recently found for FK clusters, no obvious relation emerges for generic Q between the spin cluster connectivity and the structure constants obtained from analytic continuation of the minimal model constants. The numerical results strongly suggest that spin and FK clusters are described by conformal field theories with different realizations of the color symmetry of the Potts model.