The Jordan structure of two-dimensional loop models

DOI10.1088/1742-5468/2011/04/P04007zbMath1456.82300arXiv1101.2885OpenAlexW3103140544MaRDI QIDQ3301244

Yvan Saint-Aubin, Alexi Morin-Duchesne

Publication date: 11 August 2020

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

Full work available at URL: https://arxiv.org/abs/1101.2885

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Exactly solvable models; Bethe ansatz (82B23)

Related Items (17)

Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity ⋮ Jordan blocks and the Bethe ansatz. I: The eclectic spin chain as a limit ⋮ The principal indecomposable modules of the dilute Temperley-Lieb algebra ⋮ Fusion hierarchies, T-systems and Y-systems for the dilute A2(2) loop models on a strip ⋮ Critical site percolation on the triangular lattice: from integrability to conformal partition functions ⋮ Bimodule structure of the mixed tensor product over \(\mathcal{U}_q s \ell(2 | 1)\) and quantum walled Brauer algebra ⋮ Modular invariant partition function of critical dense polymers ⋮ Kazhdan-Lusztig equivalence and fusion of Kac modules in Virasoro logarithmic models ⋮ Classification of Kac representations in the logarithmic minimal models \(LM(1,p)\) ⋮ Refined conformal spectra in the dimer model ⋮ Logarithmic superconformal minimal models ⋮ Fusion hierarchies,T-systems, andY-systems of logarithmic minimal models ⋮ Transfer matrix for spanning trees, webs and colored forests ⋮ Kac boundary conditions of the logarithmic minimal models ⋮ Conformal partition functions of critical percolation fromD₃thermodynamic Bethe Ansatz equations ⋮ Boundary algebras and Kac modules for logarithmic minimal models ⋮ Classifying integrable spin-1/2 chains with nearest neighbour interactions

Cites Work

• Unnamed Item
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• Conformal field theory at central charge \(c=0\): a measure of the indecomposability \((b)\) parameters
• Conformal boundary loop models
• Character decomposition of Potts model partition functions. I: Cyclic geometry
• Eigenvalue amplitudes of the Potts model on a torus
• On the percolation BCFT and the crossing probability of Watts
• Conformal two-boundary loop model on the annulus
• Infinite conformal symmetry in two-dimensional quantum field theory
• Hecke algebras of type \(A_ n\) and subfactors
• The Temperley-Lieb algebra at roots of unity
• Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy.
• Index for subfactors
• Exact results for the universal area distribution of clusters in percolation, Ising, and Potts models
• The representation theory of the Temperley-Lieb algebras
• Logarithmic operators in conformal field theory
• Graph theory and statistical physics
• Critical percolation in finite geometries
• Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits
• Integrable boundary conditions and {\cal W} -extended fusion in the logarithmic minimal models {\cal LM}(1\hbox{,}\, p)
• PTsymmetry of the non-Hermitian XX spin-chain: non-local bulk interaction from complex boundary fields
• On staggered indecomposable Virasoro modules
• Equivalence of the Potts model or Whitney polynomial with an ice-type model
• Conformal invariance in two-dimensional percolation
• Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134)
• A crossing probability for critical percolation in two dimensions
• BITS AND PIECES IN LOGARITHMIC CONFORMAL FIELD THEORY
• FUSION OF A-D-E LATTICE MODELS
• Logarithmic minimal models
• Combinatorial aspects of boundary loop models
• Inhomogeneous loop models with open boundaries
• PT symmetry on the lattice: the quantum group invariantXXZspin chain
• The Spontaneous Magnetization of a Two-Dimensional Ising Model
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions

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