An exact solution of a two-dimensional, non-Baxter-type vertex model

S Wang

In this paper, we obtain all solutions of Yang-Baxter equation with spectral parameter for six-vertex model in theory of exactly solved statistical models by four sets of non-degenarate basic solutions and seven sets of degenerate basic solutions up to five solution transformations. The unitary condition of the solutions is also discussed.

R. Z. Bariev

Kiyoshi Sogo, M. Uchinami, Yuko Akutsu +1 more

In the case of two-component models, all possible solutions for factorization equations of S-matrix are obtained. These solutions give a classification of solvable vertex models. It is found that Yang-Baxter relation is more general than the factorization equation. The six vertex model by Yang, Yang and Sutherland is derived not from the factorization equation but from Yang-Baxter relation. Thus it is concluded that Yang-Baxter relation lies at the basis of all the known solvable two component models. Furthermore, spin Hamiltonians corresponding to our vertex models are presented in explicit forms.

Esther Lopes

Cong-xin Liu, Ju Guo-Xing, Shikun Wang +1 more

The symmetries, especially those related to the R -transformation, of the reflection equation (RE) for two-component systems are analysed. The classification of solutions to the RE for eight-, six- and seven-vertex-type R -matrices is given. All solutions can be obtained from those corresponding to the standard R -matrices by K -transformation. For the free-fermion models, the boundary matrices have property tr K + (0) = 0, and the free-fermion-type R -matrix with the same symmetry as that of a Baxter type corresponds to the same form of a K - -matrix for the Baxter type. We present the Hamiltonians for the open spin systems connected with our solutions. In particular, the boundary Hamiltonian of seven-vertex models is obtained with a generalization to the Sklyanin formalism.

Anderson Almeida Ferreira, Francisco Castilho Alcaraz