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

We consider the six-vertex model with anti-periodic boundary conditions across a finite strip. The row-to-row transfer matrix is diagonalized 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.