  We investigate the triangular-lattice antiferromagnetic Ising model with a
spatially anisotropic next-nearest-neighbor ferromagnetic coupling, which was
first discussed by Kitatani and Oguchi. By employing the effective geometric
factor, we analyze the scaling dimensions of the operators around the
Berezinskii-Kosterlitz-Thouless (BKT) transition lines, and determine the
global phase diagram. Our numerical data exhibit that two types of
BKT-transition lines separate the intermediate critical region from the ordered
and disordered phases, and they do not merge into a single curve in the
antiferromagnetic region. We also estimate the central charge and perform some
consistency checks among scaling dimensions in order to provide the evidence of
the six-state clock universality. Further, we provide an analysis of the shapes
of boundaries based on the crossover argument.
