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

TL;DR

This study maps the phase diagram of a triangular antiferromagnetic Ising model with anisotropic next-nearest-neighbor coupling, revealing BKT transitions and confirming six-state clock universality through level-spectroscopy analysis.

Contribution

It introduces a detailed phase diagram and confirms the six-state clock universality in the model using a level-spectroscopy approach.

Findings

Identification of two BKT transition lines separating critical, ordered, and disordered phases.

Estimation of central charge consistent with universality class.

Analysis of boundary shapes based on crossover arguments.

Abstract

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.