Partition function of the eight-vertex model with domain wall boundary condition

Abstract

We derive the recursive relations of the partition function for the eight-vertex model on an $N\times N$ square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain wall partition function of the model. In the trigonometric/rational limit, our results recover the corresponding ones for the six-vertex model.

Latex file, 20 pages; V2, references added

References in corpus (10)

• Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase
• $T$-$Q$ relation and exact solution for the XYZ chain with general nondiagonal boundary terms
• SOS model partition function and the elliptic weight functions
• $Z_n$ elliptic Gaudin model with open boundaries
• Supersymmetric Vertex Models with Domain Wall Boundary Conditions
• Multiple reference states and complete spectrum of the $Z_n$ Belavin model with open boundaries
• Higher spin vertex models with domain wall boundary conditions
• Two elliptic height models with factorized domain wall partition functions
• Factorized domain wall partition functions in trigonometric vertex models
• Three-coloring statistical model with domain wall boundary conditions. II. Trigonometric limit

Cited by in corpus (10)

• Multiple integral representation for the trigonometric SOS model with domain wall boundaries
• Refined functional relations for the elliptic SOS model
• Domain wall partition function of the eight-vertex model with a non-diagonal reflecting end
• Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis
• Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end
• Functional relations and the Yang-Baxter algebra
• Elliptic supersymmetric integrable model and multivariable elliptic functions
• Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions
• Scalar products of the elliptic Felderhof model and elliptic Cauchy formula
• Elliptic free-fermion model with OS boundary and elliptic Pfaffians