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

TL;DR

This study uses level spectroscopy to analyze the phase diagram of the square-lattice three-state Potts model with ferromagnetic next-nearest-neighbor coupling, revealing an extended massless region and confirming universal excitation relations.

Contribution

It provides a precise numerical analysis of the phase diagram and clarifies the extent of the massless region, challenging previous finite-size scaling results.

Findings

Massless region extends up to the decoupling point with Z3×Z3 criticality.

Universal relations among excitation levels are verified.

The phase diagram is precisely determined using level spectroscopy.

Abstract

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 ${\bf Z}_3\times{\bf Z}_3$ criticality in the antiferromagnetic region. We also check the universal relations among excitation levels to provide the reliability of our result.