Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions

Abstract

We consider the six-vertex model with anti-periodic boundary conditions across a finite strip. The row-to-row transfer matrix is diagonalised by the `commuting transfer matrices' method. {}From the exact solution we obtain an independent derivation of the interfacial tension of the six-vertex model in the anti-ferroelectric phase. The nature of the corresponding integrable boundary condition on the $XXZ$ spin chain is also discussed.

18 pages, LaTeX with 1 PostScript figure

Cited by in corpus (52)

• Thermodynamic limit of the Six-Vertex Model with Domain Wall Boundary Conditions
• Off-diagonal Bethe ansatz and exact solution of a topological spin ring
• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
• Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators
• Boundary correlation functions of the six-vertex model
• Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase
• Dissipative quantum Ising chain as a non-Hermitian Ashkin-Teller model
• Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model
• Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• The XXZ model with anti-periodic twisted boundary conditions
• Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
• The $Z_2$ staggered vertex model and its applications
• Slavnov and Gaudin-Korepin Formulas for Models without $\mathrm{U}(1)$ Symmetry: the Twisted XXX Chain
• Boundary polarization in the six-vertex model
• Exact solution of the six-vertex model with domain wall boundary condition. Critical line between ferroelectric and disordered phases
• Exact solution of the six-vertex model with domain wall boundary conditions. Antiferroelectric phase
• Commuting difference operators with elliptic coefficients from Baxter's vacuum vestors
• Exact ground state and elementary excitations of a topological spin chain
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• On quantum separation of variables beyond fundamental representations
• Complete spectrum of quantum integrable lattice models associated to ${\mathcal{U}}_q(\widehat{g{l}_n})$ by separation of variables
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Phase separation in the six-vertex model with a variety of boundary conditions
• Exact solution of the $D_3$ non-Abelian anyon chain
• Integrable SU(N) vertex models with general toroidal boundary conditions
• An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
• Non-diagonal boundary conditions for gl(1|1) super spin chains
• Influence of boundary conditions on bulk properties of six-vertex model
• Correlation functions by Separation of Variables: the XXX spin chain
• The entropy of the six-vertex model with variety of different boundary conditions
• Thermodynamic limit and twisted boundary energy of the XXZ spin chain with antiperiodic boundary condition
• Twisted Heisenberg chain and the six-vertex model with DWBC
• Exact solution of an su(n) spin torus
• Mixed integrable SU(N) vertex model with arbitrary twists
• Nested algebraic Bethe ansatz for open spin chains with even twisted Yangian symmetry
• Six - Vertex Model with Domain wall boundary conditions. Variable inhomogeneities
• Thermodynamic limit and boundary energy of the spin-1 Heisenberg chain with non-diagonal boundary fields
• Thermodynamic limit of the spin-$\frac{1}{2}$ XYZ spin chain with the antiperiodic boundary condition
• Exact solution of a anisotropic $J_1-J_2$ spin chain with antiperiodic boundary condition
• A universal graph description for one-dimensional exchange models
• Boundary correlations for the six-vertex model with reflecting end boundary condition
• Arctic curve of the free-fermion six-vertex model with reflecting end boundary condition
• Correlation functions of the XXZ spin chain with the twisted boundary condition
• Domain-wall boundaries through non-diagonal twists in the six-vertex model
• Finite-size spectrum of the staggered six-vertex model with antidiagonal boundary conditions
• Scattering matrix of elementary excitations in the antiperiodic XXZ spin chain with η=iπ/3
• T-W relation and free energy of the antiperiodic XXZ chain with η=iπ/3 at a finite temperature
• On the solutions of the $Z_n$-Belavin model with arbitrary number of sites