Combinatorial aspects of boundary loop models

DOI10.1088/1742-5468/2008/01/P01021zbMath1456.82275arXiv0709.0812MaRDI QIDQ5239425

Jesper Lykke Jacobsen, Hubert Saleur

Publication date: 22 October 2019

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.0812

zbMATH Keywords

conformal field theoryalgebraic structures of integrable modelsloop models and polymersboundary solvable models

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Continuum limits in quantum field theory (81T27) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items (11)

Conformal boundary conditions in the critical \({\mathcal O}(n)\) model and dilute loop models ⋮ Boundary transitions of the \(O(n)\) model on a dynamical lattice ⋮ Algebraic Bethe ansatz for the open XXZ spin chain with non-diagonal boundary terms via \(U_{\mathfrak{q}}\mathfrak{sl}_2\) symmetry ⋮ A physical approach to the classification of indecomposable Virasoro representations from the blob algebra ⋮ Operator content of the critical Potts model in \(d\) dimensions and logarithmic correlations ⋮ Is the five-flow conjecture almost false? ⋮ The exact finite size ground state of the O(n= 1) loop model with open boundaries ⋮ The Jordan structure of two-dimensional loop models ⋮ Edge states and conformal boundary conditions in super spin chains and super sigma models ⋮ Conformal two-boundary loop model on the annulus ⋮ Conformal Field Theory Applied to Loop Models

Cites Work

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• Conformal boundary loop models
• The determinant of the Gram matrix for a Specht module
• Character decomposition of Potts model partition functions. I: Cyclic geometry
• The two-boundary Temperley-Lieb algebra.
• Meander determinants
• The blob algebra and the periodic Temperley-Lieb algebra
• Meanders and the Temperley-Lieb algebra
• On the structure of the blob algebra
• Enlarged symmetry algebras of spin chains, loop models, and \(S\)-matrices
• Towers of recollement and bases for diagram algebras: planar diagrams and a little beyond.
• Loops, matchings and alternating-sign matrices
• Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products

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