  Comprehensive studies are made on the six-state clock universality of two
models using several approaches. We apply the machine-learning technique of
phase classification to the antiferromagnetic (AF) three-state Potts model on
the square lattice with ferromagnetic next-nearest-neighbor (NNN) coupling and
the triangular AF Ising model with anisotropic NNN coupling to study two
Berezinskii-Kosterlitz-Thouless transitions. We also use the Monte Carlo
simulation paying attention to the ratio of correlation functions of different
distances for these two models. The obtained results are compared with those of
the previous studies using the level-spectroscopy method. We directly show the
six-state clock universality for totally different systems with the
machine-learning study.
