Nuclear Physics, Section B, ISSN 0550-3213, 05/2014, Volume 882, Issue 1, pp. 70 - 96

In this paper we review the theory of the Yangâ€“Baxter equation related to the 6-vertex model and its higher spin generalizations. We employ a 3D approach to...

CHIRAL POTTS-MODEL | XXX SPIN CHAIN | CONFORMAL FIELD-THEORY | Q-OPERATOR | ARBITRARY SPIN | R-MATRIX | ANISOTROPIC HEISENBERG CHAIN | 8-VERTEX MODEL | LATTICE STATISTICS | INTEGRABLE STRUCTURE | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Mathematics - Quantum Algebra | Mathematical Physics | Nuclear and High Energy Physics | High Energy Physics - Theory

CHIRAL POTTS-MODEL | XXX SPIN CHAIN | CONFORMAL FIELD-THEORY | Q-OPERATOR | ARBITRARY SPIN | R-MATRIX | ANISOTROPIC HEISENBERG CHAIN | 8-VERTEX MODEL | LATTICE STATISTICS | INTEGRABLE STRUCTURE | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Mathematics - Quantum Algebra | Mathematical Physics | Nuclear and High Energy Physics | High Energy Physics - Theory

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 09/2017, Volume 50, Issue 39, p. 395001

We survey and enlarge the known mappings of the 16-vertex model, with emphasis on mappings between the even and odd 8-vertex subcases of the general model,...

free-fermion model | 16-vertex model | 8-vertex model | odd 8-vertex model | STATISTICAL-MECHANICS | ASHKIN-TELLER MODEL | PHYSICS, MULTIDISCIPLINARY | 2-DIMENSIONAL ISING-MODEL | PHYSICS, MATHEMATICAL | 16 VERTEX MODEL | EXACTLY SOLVABLE MODELS | UNION JACK LATTICE | RANGE 2-SPIN INTERACTION | 3-SPIN INTERACTIONS | MAGNETIC-FIELD

free-fermion model | 16-vertex model | 8-vertex model | odd 8-vertex model | STATISTICAL-MECHANICS | ASHKIN-TELLER MODEL | PHYSICS, MULTIDISCIPLINARY | 2-DIMENSIONAL ISING-MODEL | PHYSICS, MATHEMATICAL | 16 VERTEX MODEL | EXACTLY SOLVABLE MODELS | UNION JACK LATTICE | RANGE 2-SPIN INTERACTION | 3-SPIN INTERACTIONS | MAGNETIC-FIELD

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 10/2018, Volume 363, Issue 1, pp. 59 - 96

In this work we relate the spectral problem of the toroidal six-vertex modelâ€™s transfer matrix with the theory of integrable non-linear differential equations....

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | TRIANGLE EQUATIONS | SPIN | STATISTICS | MATRICES | ALGEBRA | TRIGONOMETRIC SOLUTIONS | REPRESENTATION | 8-VERTEX MODEL | PHYSICS, MATHEMATICAL | FUNCTIONAL RELATIONS | ENTROPY | Analysis | Algebra | Differential equations

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | TRIANGLE EQUATIONS | SPIN | STATISTICS | MATRICES | ALGEBRA | TRIGONOMETRIC SOLUTIONS | REPRESENTATION | 8-VERTEX MODEL | PHYSICS, MATHEMATICAL | FUNCTIONAL RELATIONS | ENTROPY | Analysis | Algebra | Differential equations

Journal Article

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, ISSN 1742-5468, 04/2019, Volume 2019, Issue 4, p. 43107

We show how the Onsager algebra, used in the original solution of the two-dimensional Ising model, arises as an infinite-dimensional symmetry of certain...

algebraic structures of integrable models | MATRIX | MECHANICS | CONFORMAL-INVARIANCE | SPIN | ANISOTROPIC HEISENBERG CHAIN | 8-VERTEX MODEL | PHYSICS, MATHEMATICAL | quantum integrability (Bethe ansatz) | LATTICE STATISTICS | symmetries of integrable models

algebraic structures of integrable models | MATRIX | MECHANICS | CONFORMAL-INVARIANCE | SPIN | ANISOTROPIC HEISENBERG CHAIN | 8-VERTEX MODEL | PHYSICS, MATHEMATICAL | quantum integrability (Bethe ansatz) | LATTICE STATISTICS | symmetries of integrable models

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 02/2013, Volume 867, Issue 3, pp. 855 - 871

In this work we refine the method presented in Galleas (2012) [1] and obtain a novel kind of functional equation determining the partition function of the...

Functional equations | Domain wall boundaries | Dynamical Yangâ€“Baxter equation | Dynamical Yang-Baxter equation | WALL BOUNDARY-CONDITIONS | ANALOG | ZUMINO-WITTEN MODELS | 8-VERTEX MODEL | 3-COLORING STATISTICAL-MODEL | LIMIT | LATTICE STATISTICS | PHYSICS, PARTICLES & FIELDS

Functional equations | Domain wall boundaries | Dynamical Yangâ€“Baxter equation | Dynamical Yang-Baxter equation | WALL BOUNDARY-CONDITIONS | ANALOG | ZUMINO-WITTEN MODELS | 8-VERTEX MODEL | 3-COLORING STATISTICAL-MODEL | LIMIT | LATTICE STATISTICS | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 11/2006, Volume 2006, Issue 11, pp. P11017 - P11017

Working in the dense loop representation, we use the planar Temperley-Lieb algebra to build integrable lattice models called logarithmic minimal models...

Integrable spin chains (vertex models) | Conformal field theory | Loop models and polymers | Solvable lattice models | DISORDERED-SYSTEMS | BOUNDARY-CONDITIONS | 1-DIMENSIONAL CHAIN | conformal field theory | loop models and polymers | SPIN-SPIN INTERACTIONS | PHYSICS, MATHEMATICAL | CRITICAL EXPONENTS | solvable lattice models | MECHANICS | integrable spin chains (vertex models) | CONFORMAL FIELD-THEORY | TWO-DIMENSIONAL POTTS | 8-VERTEX SOS MODEL | CRITICAL-BEHAVIOR | TEMPERLEY-LIEB ALGEBRA

Integrable spin chains (vertex models) | Conformal field theory | Loop models and polymers | Solvable lattice models | DISORDERED-SYSTEMS | BOUNDARY-CONDITIONS | 1-DIMENSIONAL CHAIN | conformal field theory | loop models and polymers | SPIN-SPIN INTERACTIONS | PHYSICS, MATHEMATICAL | CRITICAL EXPONENTS | solvable lattice models | MECHANICS | integrable spin chains (vertex models) | CONFORMAL FIELD-THEORY | TWO-DIMENSIONAL POTTS | 8-VERTEX SOS MODEL | CRITICAL-BEHAVIOR | TEMPERLEY-LIEB ALGEBRA

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2016, Volume 49, Issue 15, p. 154005

Using a corner transfer matrix approach, we compute the bipartite entanglement Renyi entropy in the off-critical perturbations of non-unitary conformal minimal...

entanglement in spin chains | conformal field theory | integrable lattice models | conformal field thoery | IDENTITIES | PHYSICS, MULTIDISCIPLINARY | FIELD-THEORIES | 8-VERTEX SOS MODEL | SYSTEMS | POINT | PHYSICS, MATHEMATICAL

entanglement in spin chains | conformal field theory | integrable lattice models | conformal field thoery | IDENTITIES | PHYSICS, MULTIDISCIPLINARY | FIELD-THEORIES | 8-VERTEX SOS MODEL | SYSTEMS | POINT | PHYSICS, MATHEMATICAL

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 12/2017, Volume 193, Issue 3, pp. 1811 - 1825

We consider the critical nonunitary minimal model M(3, 5) with integrable boundaries and analyze the patterns of zeros of the eigenvalues of the transfer...

nonunitary minimal model | Theoretical, Mathematical and Computational Physics | Yangâ€“Baxter integrability | lattice model | conformal field theory | Applications of Mathematics | M(3,5) model | Physics | TBA EQUATIONS | PHYSICS, MULTIDISCIPLINARY | TRICRITICAL HARD SQUARES | PHYSICS, MATHEMATICAL | EXCITED-STATES | CORNER TRANSFER-MATRICES | Yang-Baxter integrability | DELTA-FUNCTION INTERACTION | 8-VERTEX SOS MODEL | ISING-MODEL | SOLVABLE LATTICE MODELS | CONFORMAL FIELD-THEORIES | THERMODYNAMIC BETHE-ANSATZ | Thermodynamics | Models

nonunitary minimal model | Theoretical, Mathematical and Computational Physics | Yangâ€“Baxter integrability | lattice model | conformal field theory | Applications of Mathematics | M(3,5) model | Physics | TBA EQUATIONS | PHYSICS, MULTIDISCIPLINARY | TRICRITICAL HARD SQUARES | PHYSICS, MATHEMATICAL | EXCITED-STATES | CORNER TRANSFER-MATRICES | Yang-Baxter integrability | DELTA-FUNCTION INTERACTION | 8-VERTEX SOS MODEL | ISING-MODEL | SOLVABLE LATTICE MODELS | CONFORMAL FIELD-THEORIES | THERMODYNAMIC BETHE-ANSATZ | Thermodynamics | Models

Journal Article

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, 07/2019, Volume 52, Issue 28

The mutually commuting 1 x n fused single and double-row transfer matrices of the critical six-vertex model are considered at roots of unity q = e(i lambda)...

INTEGRABLE MODELS | PHYSICS, MULTIDISCIPLINARY | Bethe ansatz equations | BOUNDARY-CONDITIONS | dense loop models | OPEN XXZ CHAIN | 8-VERTEX MODEL | PHYSICS, MATHEMATICAL | FUNCTIONAL RELATIONS | exactly solvable models | Q-OPERATOR | ANISOTROPIC HEISENBERG CHAIN | TEMPERLEY-LIEB ALGEBRAS | THERMODYNAMIC BETHE-ANSATZ | LATTICE STATISTICS | vertex models

INTEGRABLE MODELS | PHYSICS, MULTIDISCIPLINARY | Bethe ansatz equations | BOUNDARY-CONDITIONS | dense loop models | OPEN XXZ CHAIN | 8-VERTEX MODEL | PHYSICS, MATHEMATICAL | FUNCTIONAL RELATIONS | exactly solvable models | Q-OPERATOR | ANISOTROPIC HEISENBERG CHAIN | TEMPERLEY-LIEB ALGEBRAS | THERMODYNAMIC BETHE-ANSATZ | LATTICE STATISTICS | vertex models

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 10/2013, Volume 88, Issue 4, p. 042117

Many critical properties of the Hintermann-Merlini model are known exactly through the mapping to the eight-vertex model. Wu [J. Phys. C 8, 2262 (1975)]...

MONTE-CARLO | BAXTER-WU MODEL | STATISTICS | PHYSICS, FLUIDS & PLASMAS | ISING-MODEL | 8-VERTEX MODEL | POTTS-MODEL | CRITICAL-BEHAVIOR | PHYSICS, MATHEMATICAL | LATTICE | CRITICAL EXPONENTS | RENORMALIZATION | Physics - Statistical Mechanics

MONTE-CARLO | BAXTER-WU MODEL | STATISTICS | PHYSICS, FLUIDS & PLASMAS | ISING-MODEL | 8-VERTEX MODEL | POTTS-MODEL | CRITICAL-BEHAVIOR | PHYSICS, MATHEMATICAL | LATTICE | CRITICAL EXPONENTS | RENORMALIZATION | Physics - Statistical Mechanics

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 4/2015, Volume 2015, Issue 4, pp. 1 - 43

We consider the non-unitary Lee-Yang minimal model â„³2,5 $$ \mathrm{\mathcal{M}}\left(2,\;5\right) $$ in three different finite geometries: (i) on the interval...

Lattice Integrable Models | Integrable Field Theories | Field Theories in Lower Dimensions | Lattice Quantum Field Theory | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | TBA EQUATIONS | CORNER TRANSFER MATRICES | TRICRITICAL HARD SQUARES | BOUNDARY-CONDITIONS | DELTA-FUNCTION INTERACTION | 8-VERTEX SOS MODEL | ISING-MODEL | SOLVABLE LATTICE MODELS | CONFORMAL FIELD-THEORIES | Field Theory | THERMODYNAMIC BETHE-ANSATZ | Lattice Quantum | PHYSICS, PARTICLES & FIELDS | Thermodynamics | Models | Atmospheric physics | Analysis | Physics - High Energy Physics - Theory | Nuclear and High Energy Physics | High Energy Physics - Theory

Lattice Integrable Models | Integrable Field Theories | Field Theories in Lower Dimensions | Lattice Quantum Field Theory | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | TBA EQUATIONS | CORNER TRANSFER MATRICES | TRICRITICAL HARD SQUARES | BOUNDARY-CONDITIONS | DELTA-FUNCTION INTERACTION | 8-VERTEX SOS MODEL | ISING-MODEL | SOLVABLE LATTICE MODELS | CONFORMAL FIELD-THEORIES | Field Theory | THERMODYNAMIC BETHE-ANSATZ | Lattice Quantum | PHYSICS, PARTICLES & FIELDS | Thermodynamics | Models | Atmospheric physics | Analysis | Physics - High Energy Physics - Theory | Nuclear and High Energy Physics | High Energy Physics - Theory

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 10/2015, Volume 899, Issue C, pp. 677 - 769

Virasoro Kac modules were originally introduced indirectly as representations whose characters arise in the continuum scaling limits of certain transfer...

BLOB ALGEBRA | GL(1-VERTICAL-BAR-1) SPIN CHAIN | CONFORMAL FIELD-THEORY | VERLINDE FORMULAS | VIRASORO REPRESENTATIONS | FUSION ALGEBRAS | LATTICE MODELS | 8-VERTEX SOS MODEL | HECKE ALGEBRAS | TEMPERLEY-LIEB ALGEBRA | PHYSICS, PARTICLES & FIELDS | Projectors | Models | Algebra | Analysis | High Energy Physics | Mathematical Physics | Nuclear and High Energy Physics | Theory | Nuclear and particle physics. Atomic energy. Radioactivity | Condensed Matter - Statistical Mechanics | Quantum Algebra | Mathematics | High Energy Physics - Theory | Representation Theory

BLOB ALGEBRA | GL(1-VERTICAL-BAR-1) SPIN CHAIN | CONFORMAL FIELD-THEORY | VERLINDE FORMULAS | VIRASORO REPRESENTATIONS | FUSION ALGEBRAS | LATTICE MODELS | 8-VERTEX SOS MODEL | HECKE ALGEBRAS | TEMPERLEY-LIEB ALGEBRA | PHYSICS, PARTICLES & FIELDS | Projectors | Models | Algebra | Analysis | High Energy Physics | Mathematical Physics | Nuclear and High Energy Physics | Theory | Nuclear and particle physics. Atomic energy. Radioactivity | Condensed Matter - Statistical Mechanics | Quantum Algebra | Mathematics | High Energy Physics - Theory | Representation Theory

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 02/2010, Volume 43, Issue 8, pp. 085202 - 085202

Belavin's (Z/nZ)-symmetric model is considered on the basis of bosonization of vertex operators in the A(n-1)((1)) model and vertex-face transformation....

BOSONIZATION | FREE-FIELD CONSTRUCTION | PHYSICS, MULTIDISCIPLINARY | 8-VERTEX MODEL | PHYSICS, MATHEMATICAL | ELLIPTIC ALGEBRA | PROBABILITIES | Operators | Construction | Integrals | Ground state | Mathematical models | Transformations | Representations | Form factors

BOSONIZATION | FREE-FIELD CONSTRUCTION | PHYSICS, MULTIDISCIPLINARY | 8-VERTEX MODEL | PHYSICS, MATHEMATICAL | ELLIPTIC ALGEBRA | PROBABILITIES | Operators | Construction | Integrals | Ground state | Mathematical models | Transformations | Representations | Form factors

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2012, Volume 45, Issue 8, pp. 85001 - 19

The corner transfer matrix renormalization group method is an efficient method for evaluating physical quantities in statistical mechanical models. It...

CHIRAL POTTS-MODEL | STATISTICAL-MECHANICS | LATTICE ISING-MODEL | PHYSICS, MULTIDISCIPLINARY | ALGORITHM | 3D CLASSICAL-MODELS | GAS | 8-VERTEX MODEL | PHYSICS, MATHEMATICAL | VARIATIONAL APPROXIMATION | Renormalization group methods | Partitions | Singularities | Mathematical analysis | Series expansion | Mathematical models | Corners

CHIRAL POTTS-MODEL | STATISTICAL-MECHANICS | LATTICE ISING-MODEL | PHYSICS, MULTIDISCIPLINARY | ALGORITHM | 3D CLASSICAL-MODELS | GAS | 8-VERTEX MODEL | PHYSICS, MATHEMATICAL | VARIATIONAL APPROXIMATION | Renormalization group methods | Partitions | Singularities | Mathematical analysis | Series expansion | Mathematical models | Corners

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 10/2014, Volume 887, Issue C, pp. 423 - 440

We derive exact inversion identities satisfied by the transfer matrix of inhomogeneous interaction-round-a-face (IRF) models with arbitrary boundary conditions...

XXZ SPIN CHAIN | FIELD-THEORY | 8-VERTEX SOS MODEL | REPRESENTATION | NONDIAGONAL BOUNDARY TERMS | FUNCTIONAL RELATIONS | BETHE-ANSATZ | REFLECTION EQUATION | PHYSICS, PARTICLES & FIELDS | Mathematical Physics | Nuclear and High Energy Physics | Nuclear and particle physics. Atomic energy. Radioactivity | bethe-ansatz | reflection equation | representation | High Energy Physics - Theory | field-theory | 8-vertex sos model | nondiagonal boundary terms | functional relations | Condensed Matter - Statistical Mechanics | xxz spin chain

XXZ SPIN CHAIN | FIELD-THEORY | 8-VERTEX SOS MODEL | REPRESENTATION | NONDIAGONAL BOUNDARY TERMS | FUNCTIONAL RELATIONS | BETHE-ANSATZ | REFLECTION EQUATION | PHYSICS, PARTICLES & FIELDS | Mathematical Physics | Nuclear and High Energy Physics | Nuclear and particle physics. Atomic energy. Radioactivity | bethe-ansatz | reflection equation | representation | High Energy Physics - Theory | field-theory | 8-vertex sos model | nondiagonal boundary terms | functional relations | Condensed Matter - Statistical Mechanics | xxz spin chain

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2017, Volume 50, Issue 16, p. 164003

We construct quasi-local conserved currents in the six-vertex model with anisotropy parameter eta by making use of the quantum-group approach of Bernard and...

exactly solvable lattice models | Interaction-Round-a-Face models | quantum groups | discrete holomorphicity | CHIRAL POTTS-MODEL | COULOMB GAS | PHYSICS, MULTIDISCIPLINARY | QUANTUM-FIELD THEORY | 8-VERTEX MODEL | OPERATOR CONTENT | PHYSICS, MATHEMATICAL | HOLOMORPHIC PARAFERMIONS | CRITICAL EXPONENTS | CONFORMAL-INVARIANCE | LATTICE MODELS | ISING-MODEL

exactly solvable lattice models | Interaction-Round-a-Face models | quantum groups | discrete holomorphicity | CHIRAL POTTS-MODEL | COULOMB GAS | PHYSICS, MULTIDISCIPLINARY | QUANTUM-FIELD THEORY | 8-VERTEX MODEL | OPERATOR CONTENT | PHYSICS, MATHEMATICAL | HOLOMORPHIC PARAFERMIONS | CRITICAL EXPONENTS | CONFORMAL-INVARIANCE | LATTICE MODELS | ISING-MODEL

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 12/2007, Volume 40, Issue 49, pp. 14605 - 14647

We investigate solutions to the Bethe equations for the isotropic S = 1/2 Heisenberg chain involving complex, string-like rapidity configurations of arbitrary...

BETHE-ANSATZ EQUATIONS | LESS-THAN 1 | THERMODYNAMICS | XXZ SPIN CHAIN | PHYSICS, MULTIDISCIPLINARY | ISING RING | TRANSFER-MATRIX | HYPOTHESIS | 8-VERTEX MODEL | COMPLETENESS | PHYSICS, MATHEMATICAL | EXCITED-STATES

BETHE-ANSATZ EQUATIONS | LESS-THAN 1 | THERMODYNAMICS | XXZ SPIN CHAIN | PHYSICS, MULTIDISCIPLINARY | ISING RING | TRANSFER-MATRIX | HYPOTHESIS | 8-VERTEX MODEL | COMPLETENESS | PHYSICS, MATHEMATICAL | EXCITED-STATES

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2016, Volume 49, Issue 18, p. 184002

We consider the Forrester-Baxter RSOS lattice models with crossing parameter lambda = (m'-m)pi/m' in Regime III. In the continuum scaling limit, these models...

exactly solvable models | conformal field theory | lattice models | PHYSICS, MULTIDISCIPLINARY | HARD HEXAGON MODEL | PHYSICS, MATHEMATICAL | LEE EDGE SINGULARITY | CORNER TRANSFER-MATRICES | VIRASORO ALGEBRAS | CONFORMAL FIELD-THEORY | SCALING 3-STATE POTTS | 8-VERTEX SOS MODEL | GAS GENERALIZATION | LOCAL HEIGHT PROBABILITIES | 2 DIMENSIONS

exactly solvable models | conformal field theory | lattice models | PHYSICS, MULTIDISCIPLINARY | HARD HEXAGON MODEL | PHYSICS, MATHEMATICAL | LEE EDGE SINGULARITY | CORNER TRANSFER-MATRICES | VIRASORO ALGEBRAS | CONFORMAL FIELD-THEORY | SCALING 3-STATE POTTS | 8-VERTEX SOS MODEL | GAS GENERALIZATION | LOCAL HEIGHT PROBABILITIES | 2 DIMENSIONS

Journal Article