Global phase diagram and six-state clock universality behavior in the triangular antiferromagnetic Ising model with anisotropic next-nearest-neighbor coupling: level-spectroscopy approach.

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.

Level spectroscopy of the square-lattice three-state Potts model with a ferromagnetic next-nearest-neighbor coupling.

We study the square-lattice three-state Potts model with the ferromagnetic next-nearest-neighbor coupling at finite temperature. Using the level-spectroscopy method, we numerically analyze the excitation spectrum of the transfer matrices and precisely determine the global phase diagram. Then we find that, contrary to a previous result based on the finite-size scaling, the massless region continues up to the decoupling point with Z3 x Z3 criticality in the antiferromagnetic region. We also check the universal relations among excitation levels to provide the reliability of our result.