Study of the Fully Frustrated Clock Model using the Wang-Landau Algorithm

TL;DR

This study uses the Wang-Landau algorithm to investigate phase transitions in the fully frustrated six-state clock model on a triangular lattice, confirming multiple Kosterlitz-Thouless and chiral transitions with universal critical exponents.

Contribution

It applies the Wang-Landau algorithm to analyze the frustrated clock model, providing detailed estimates of transition temperatures and critical exponents, supporting the double transition scenario.

Findings

Confirmed the existence of multiple KT and chiral phase transitions.

Estimated critical temperatures with high precision.

Found universal decay exponents for KT transitions in the frustrated model.

Abstract

Monte Carlo simulations using the newly proposed Wang-Landau algorithm together with the broad histogram relation are performed to study the antiferromagnetic six-state clock model on the triangular lattice, which is fully frustrated. We confirm the existence of the magnetic ordering belonging to the Kosterlitz-Thouless (KT) type phase transition followed by the chiral ordering which occurs at slightly higher temperature. We also observe the lower temperature phase transition of KT type due to the discrete symmetry of the clock model. By using finite-size scaling analysis, the higher KT temperature $T_2$ and the chiral critical temperature $T_c$ are respectively estimated as $T_2=0.5154(8)$ and $T_c=0.5194(4)$. The results are in favor of the double transition scenario. The lower KT temperature is estimated as $T_1=0.496(2)$. Two decay exponents of KT transitions corresponding to higher and lower temperatures are respectively estimated as $\eta_2=0.25(1)$ and $\eta_1=0.13(1)$, which suggests that the exponents associated with the KT transitions are universal even for the frustrated model.