  We investigate the interacting domain-wall model derived from the
triangular-lattice antiferromagnetic Ising model with two next-nearest-neighbor
interactions. The system has commensurate phases with a domain-wall density
$q=2/3$ as well as that of $q=0$ when the interaction is repulsive. The $q=2/3$
commensurate phase is separated from the incommensurate phase through the
Kosterlitz--Thouless~(KT) transition. The critical interaction strength and the
nature of the KT phase transition are studied by the Monte Carlo simulations
and numerical transfer-matrix calculations. For strongly attractive
interaction, the system undergoes a first-order phase transition from the $q=0$
commensurate phase to the incommensurate phase with $q\neq 0$. The
incommensurate phase is a critical phase which is in the Gaussian model
universality class. The effective Gaussian coupling constant is calculated as a
function of interaction parameters from the finite-size scaling of the transfer
matrix spectra .
