arXiv:hep-th/9512218 · Journal of Physics A Mathematical and General

A construction of solutions to reflection equations for interaction-round-a-face models

Roger E. Behrend, Paul A. Pearce

Published Dec 21, 1996• 28 citations

Abstract

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency 1. Among such models are the Andrews - Baxter - Forrester models, for which we construct reflection equation solutions for fixed and free boundary conditions.

DOI: 10.1088/0305-4470/29/24/009

Related papers

Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy

Roger E. Behrend, Paul A. Pearce, David O’Brien

arXiv:hep-th/9507118Journal of Statistical PhysicsJul 1, 1996125 citations

On the fusion of face and vertex models

Yu‐Kui Zhou, Bo-Yu Hou

Some new solutions of the Yang-Baxter or star-triangle relations are found using the fusion procedure. For Belavin's (1981) z n *z n symmetric model the relation between the fusion procedure of the vertex and face models is also constructed.

Journal of Physics A Mathematical and GeneralDec 7, 198913 citations

FUSION OF A-D-E LATTICE MODELS

Yu‐Kui Zhou, Paul A. Pearce

arXiv:hep-th/9405019International Journal of Modern Physics BNov 1, 199424 citations

Integrable Boundary Conditions Associated with the Zn × Zn Belavin Model and Solutions of Reflection Equation

Heng Fan, Kangjie Shi, Bo-Yu Hou +1 more

We construct solvable models with nontrivial boundary from the well known Belavin R-matrix. The reflection equation for the boundary reflection matrix is studied and the complete solution for the one associated with the eight-vertex model is found.

International Journal of Modern Physics AJun 30, 19977 citations

General Yang-Baxterization of reflection equations and general K-matrices of An-1vertex models

Hong‐Chen Fu, Mo‐Lin Ge

General Yang-Baxterization of reflection equations for R with two distinct eigenvalues is presented. This procedure is used to construct reflection K-matrices of reflection equations for the A n-1 vertex models. (Diagonal) K-matrices by de Vege and Gonzalez-Ruiz(1993) for the A n-1 vertex model are reproduced. Furthermore, some new off-diagonal K-matrices for the A n-1 vertex model are obtained.

Journal of Physics A Mathematical and GeneralJul 7, 19943 citations

Boundary reflection matrices of massive ϕ1,3-perturbed unitary minimal models

Zoltán Bajnok, Rafael I. Nepomechie, Paul A. Pearce

A bstract We propose explicit expressions for the boundary reflection matrices of the $${\mathcal{A}}_{m}+(r, s)$$ series of massive scattering theories, obtained by perturbing the $${\mathcal{A}}_{m}$$ unitary minimal models with ( r, s ) boundary conditions with both bulk and boundary ϕ 1 , 3 operators. We identify the vacua that live on the boundary with the allowed edges of the ( r, s ) conformal boundary conditions of the A m Andrews-Baxter-Forrester model. The boundary reflection matrices are then “direct sums” of certain pairs of A m− 1 Behrend-Pearce solutions of the boundary Yang-Baxter equation and are consistent with the boundary bootstrap and the recently-introduced crossing, as well as the Z 2 (height-reversal), Kac table and non-invertible symmetries.

arXiv:2509.04286Journal of High Energy PhysicsDec 23, 20250 citations

arXiv:hep-th/9512218 · Journal of Physics A Mathematical and General

A construction of solutions to reflection equations for interaction-round-a-face models

Roger E. Behrend, Paul A. Pearce

Published Dec 21, 1996• 28 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0305-4470/29/24/009

Related papers

Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy

Roger E. Behrend, Paul A. Pearce, David O’Brien

arXiv:hep-th/9507118Journal of Statistical PhysicsJul 1, 1996125 citations

On the fusion of face and vertex models

Yu‐Kui Zhou, Bo-Yu Hou

Journal of Physics A Mathematical and GeneralDec 7, 198913 citations

FUSION OF A-D-E LATTICE MODELS

Yu‐Kui Zhou, Paul A. Pearce

Fusion hierarchies of A-D-E face models are constructed. The fused critical D, E and elliptic D models yield new solutions of the Yang-Baxter equations with bond variables on the edges of faces in addition to the spin variables on the corners. It is shown directly that the row transfer matrices of the fused models satisfy special functional equations. Intertwiners between the fused A-D-E models are constructed by fusing the cells that intertwine the elementary face weights. As an example, we calculate explicitly the fused 2×2 face weights of the 3-state Potts model associated with the D4 diagram as well as the fused intertwiner cells for the A5-D4 intertwiner. Remarkably, this 2×2 fusion yields the face weights of both the Ising model and 3-state CSOS models.Fusion hierarchies of A-D-E face models are constructed. The fused critical D, E and elliptic D models yield new solutions of the Yang-Baxter equations with bond variables on the edges of faces in addition to the spin variables on the corners. It is shown directly that the row transfer matrices of the fused models satisfy special functional equations. Intertwiners between the fused A-D-E models are constructed by fusing the cells that intertwine the elementary face weights. As an example, we calculate explicitly the fused 2×2 face weights of the 3-state Potts model associated with the D4 diagram as well as the fused intertwiner cells for the A5-D4 intertwiner. Remarkably, this 2×2 fusion yields the face weights of both the Ising model and 3-state CSOS models.

arXiv:hep-th/9405019International Journal of Modern Physics BNov 1, 199424 citations

Integrable Boundary Conditions Associated with the Zn × Zn Belavin Model and Solutions of Reflection Equation

Heng Fan, Kangjie Shi, Bo-Yu Hou +1 more

International Journal of Modern Physics AJun 30, 19977 citations

General Yang-Baxterization of reflection equations and general K-matrices of An-1vertex models

Hong‐Chen Fu, Mo‐Lin Ge

Journal of Physics A Mathematical and GeneralJul 7, 19943 citations

Boundary reflection matrices of massive ϕ1,3-perturbed unitary minimal models

Zoltán Bajnok, Rafael I. Nepomechie, Paul A. Pearce

A bstract We propose explicit expressions for the boundary reflection matrices of the ${\mathcal{A}}_{m}+(r, s)$ series of massive scattering theories, obtained by perturbing the ${\mathcal{A}}_{m}$ unitary minimal models with ( r, s ) boundary conditions with both bulk and boundary ϕ 1 , 3 operators. We identify the vacua that live on the boundary with the allowed edges of the ( r, s ) conformal boundary conditions of the A m Andrews-Baxter-Forrester model. The boundary reflection matrices are then “direct sums” of certain pairs of A m− 1 Behrend-Pearce solutions of the boundary Yang-Baxter equation and are consistent with the boundary bootstrap and the recently-introduced crossing, as well as the Z 2 (height-reversal), Kac table and non-invertible symmetries.A bstract We propose explicit expressions for the boundary reflection matrices of the $${\mathcal{A}}_{m}+(r, s)$$ series of massive scattering theories, obtained by perturbing the $${\mathcal{A}}_{m}$$ unitary minimal models with ( r, s ) boundary conditions with both bulk and boundary ϕ 1 , 3 operators. We identify the vacua that live on the boundary with the allowed edges of the ( r, s ) conformal boundary conditions of the A m Andrews-Baxter-Forrester model. The boundary reflection matrices are then “direct sums” of certain pairs of A m− 1 Behrend-Pearce solutions of the boundary Yang-Baxter equation and are consistent with the boundary bootstrap and the recently-introduced crossing, as well as the Z 2 (height-reversal), Kac table and non-invertible symmetries.

arXiv:2509.04286Journal of High Energy PhysicsDec 23, 20250 citations

A bstract We propose explicit expressions for the boundary reflection matrices of the

{\mathcal{A}}_{m}+(r, s)

series of massive scattering theories, obtained by perturbing the

{\mathcal{A}}_{m}

unitary minimal models with ( r, s ) boundary conditions with both bulk and boundary ϕ 1 , 3 operators. We identify the vacua that live on the boundary with the allowed edges of the ( r, s ) conformal boundary conditions of the A m Andrews-Baxter-Forrester model. The boundary reflection matrices are then “direct sums” of certain pairs of A m− 1 Behrend-Pearce solutions of the boundary Yang-Baxter equation and are consistent with the boundary bootstrap and the recently-introduced crossing, as well as the Z 2 (height-reversal), Kac table and non-invertible symmetries.