Comprehensive studies on the universality of BKT transitions -- Machine-learning study, Monte Carlo simulation, and Level-spectroscopy method

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.