Solutions of the boundary Yang-Baxter equation for ADE models

We present the general diagonal and, in some cases, non-diagonal solutions of the boundary Yang-Baxter equation for a number of related interaction-round-a-face models, including the standard and dilute A L , D L and E 6 , 7 , 8 models.

[1]  M. Batchelor,et al.  Exact solution and surface critical behaviour of open cyclic SOS lattice models , 1996, cond-mat/9602078.

[2]  V. Fridkin,et al.  Solutions of the reflection equation for face and vertex models associated with An(1), Bn(1), Cn(1), Dn(1) and An(2) , 1996, hep-th/9601051.

[3]  P. Pearce,et al.  A construction of solutions to reflection equations for interaction-round-a-face models , 1995, hep-th/9512218.

[4]  P. Pearce,et al.  Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy , 1995, hep-th/9507118.

[5]  P. Kulish.  Yang-Baxter equation and reflection equations in integrable models , 1995, hep-th/9507070.

[6]  H. Fan,et al.  General solution of reflection equation for eight-vertex SOS model , 1995 .

[7]  P. Pearce,et al.  Multi-colour braid-monoid algebras , 1993, hep-th/9303161.

[8]  Nienhuis,et al.  New construction of solvable lattice models including an Ising model in a field. , 1992, Physical review letters.

[9]  J. Zuber,et al.  SU($N$) Lattice Integrable Models Associated With Graphs , 1990 .

[10]  R. Baxter.  Eight-Vertex Model in Lattice Statistics and One-Dimensional Anisotropic Heisenberg Chain: II. Equivalence to a Generalized Ice-type Lattice Model , 1990 .

[11]  P. Roche.  Ocneanu cell calculus and integrable lattice models , 1990 .

[12]  E. Sklyanin.  Boundary conditions for integrable quantum systems , 1988 .

[13]  Aleksander L Owczarek,et al.  A class of interaction-round-a-face models and its equivalence with an ice-type model , 1987 .

[14]  Vincent Pasquier,et al.  Two-dimensional critical systems labelled by Dynkin diagrams , 1987 .

[15]  R. Baxter.  Exactly solved models in statistical mechanics , 1982 .

[16]  R. Baxter.  Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. II. Equivalence to a generalized ice-type lattice model , 1973 .

[17]  Elliott H Lieb,et al.  Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.