2014/02/28 by I T Alam, Murray T. Batchelor, M T Batchelor · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Boundary value problem #Class (philosophy) #Combinatorics #Computer science #Context (archaeology) #Embedding #Geology #Inversion (geology) #Lattice (music) #Loop (graph theory) #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Observable #Physics #Planar #Pure mathematics #Quantum mechanics #Statistical physics #Theoretical physics #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/47/21/215201
published as J. Phys. A: Math. Theor. 47 (2014) 215201 · 18 pages, 11 figures, minor changes, references updated
arxiv created 2014/03/27 · openalex publication_date 2014/05/07 · arxiv updated 2014/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we explore the relationship between integrability and the discrete holomorphicity of a class of complex lattice observables in the context of the Potts dense loop model and the O(n) dilute loop model. It is shown that the conditions for integrability, namely, the inversion and Yang-Baxter relations, can be derived from the condition of holomorphicity of the observables. Furthermore, the Z-invariance of the models is shown to result in the invariance of the observables on the boundary of a sublattice under reshuffling of the rhombuses of its planar rhombic embedding.