### 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 the 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 favour 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 the higher and lower temperatures are respectively estimated as η_{2} = 0.25(1) and η_{1} = 0.13(1), which suggests that the exponents associated with the KT transitions are universal even for the frustrated model.

Original language | English |
---|---|

Pages (from-to) | 4219-4230 |

Number of pages | 12 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 37 |

Issue number | 14 |

DOIs | |

Publication status | Published - 2004 Apr 9 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*37*(14), 4219-4230. https://doi.org/10.1088/0305-4470/37/14/003

**Study of the fully frustrated clock model using the Wang-Landau algorithm.** / Surungan, Tasrief; Okabe, Yutaka; Tomita, Yusuke.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 37, no. 14, pp. 4219-4230. https://doi.org/10.1088/0305-4470/37/14/003

}

TY - JOUR

T1 - Study of the fully frustrated clock model using the Wang-Landau algorithm

AU - Surungan, Tasrief

AU - Okabe, Yutaka

AU - Tomita, Yusuke

PY - 2004/4/9

Y1 - 2004/4/9

N2 - 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 the finite-size scaling analysis, the higher KT temperature T2 and the chiral critical temperature Tcare respectively estimated as T2 = 0.5154(8) and Tc= 0.5194(4). The results are in favour of the double transition scenario. The lower KT temperature is estimated as T1 = 0.496(2). Two decay exponents of KT transitions corresponding to the higher and lower temperatures are respectively estimated as η2 = 0.25(1) and η1 = 0.13(1), which suggests that the exponents associated with the KT transitions are universal even for the frustrated model.

AB - 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 the finite-size scaling analysis, the higher KT temperature T2 and the chiral critical temperature Tcare respectively estimated as T2 = 0.5154(8) and Tc= 0.5194(4). The results are in favour of the double transition scenario. The lower KT temperature is estimated as T1 = 0.496(2). Two decay exponents of KT transitions corresponding to the higher and lower temperatures are respectively estimated as η2 = 0.25(1) and η1 = 0.13(1), which suggests that the exponents associated with the KT transitions are universal even for the frustrated model.

UR - http://www.scopus.com/inward/record.url?scp=2142751541&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2142751541&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/37/14/003

DO - 10.1088/0305-4470/37/14/003

M3 - Article

VL - 37

SP - 4219

EP - 4230

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 14

ER -