  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 Pokrovsky--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
non-interacting 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. (TO APPEAR IN PHY. REV. E)
