Interacting domain walls and the five-vertex model

We investigate the thermodynamic and critical properties of an interacting-domain-wall model which is derived from the triangular-lattice antiferromagnetic Ising model with the anisotropic nearest- and next-nearest-neighbor interactions. The model is equivalent to the general five-vertex model. Diagonalizing the transfer matrix exactly by the Bethe Ansatz method, we obtain the phase diagram displaying the commensurate and incommensurate (IC) phases separated by the Pokrovksy-Talapov transitions. The phase diagram exhibits commensurate phases where the domain-wall density q is locked at the values of 0, 1/2, and 1. The IC phase is a critical state described by the Gaussian fixed point. The effective Gaussian coupling constant is obtained analytically and numerically for the IC phase using the finite-size-scaling predictions of the conformal-field theory. It takes the value 1/2 in the noninteracting limit and also at the boundaries of q=0 or 1 phase and the value 2 at the boundary of q=1/2 phase, while it varies smoothly throughout the IC region.