Loop models and their critical points

2006/09/30 by Paul Fendley
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #math.PR

paper · pdf · doi:10.1088/0305-4470/39/50/011

published as J.Phys.A39:15445,2006 · 20 pages, 15 figures

arxiv created 2006/11/29 · openalex publication_date 2006/11/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Loop models have been widely studied in physics and mathematics, in problems ranging from polymers to topological quantum computation to Schramm–Loewner evolution. I present new loop models which have critical points described by conformal field theories. Examples include both fully packed and dilute loop models with critical points described by the superconformal minimal models and the SU (2) 2 WZW models. The dilute loop models are generalized to include SU (2) k models as well.

Citations

• Current algebra and Wess-Zumino model in two dimensions
• Competing density-wave orders in a one-dimensional hard-boson model
• Infinite conformal symmetry in two-dimensional quantum field theory
• Stochastic Loewner Evolution for Conformal Field Theories with Lie Group Symmetries
• Fault-tolerant quantum computation by anyons