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

Tasrief Surungan, Yutaka Okabe, Yusuke Tomita

Research output: Contribution to journalArticle

16 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)4219-4230
Number of pages12
JournalJournal of Physics A: Mathematical and General
Volume37
Issue number14
DOIs
Publication statusPublished - 2004 Apr 9
Externally publishedYes

Fingerprint

clocks
Clocks
Temperature
exponents
Phase transitions
histograms
critical temperature
Magnetization
scaling
temperature
symmetry
decay
simulation

ASJC Scopus subject areas

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

Cite this

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

In: Journal of Physics A: Mathematical and General, Vol. 37, No. 14, 09.04.2004, p. 4219-4230.

Research output: Contribution to journalArticle

@article{7d5edfc7a05b4b6cb147e846a746ae7d,
title = "Study of the fully frustrated clock model using the Wang-Landau algorithm",
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 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.",
author = "Tasrief Surungan and Yutaka Okabe and Yusuke Tomita",
year = "2004",
month = "4",
day = "9",
doi = "10.1088/0305-4470/37/14/003",
language = "English",
volume = "37",
pages = "4219--4230",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing Ltd.",
number = "14",

}

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 -