### Abstract

We extend the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm to the study of systems with the vector order parameter. Wolff's idea of the embedded cluster formalism is used for assigning clusters. The Kosterlitz-Thouless (KT) transitions for the two-dimensional (2D) XY and q-state clock models are studied by using the PCC algorithm. Combined with the finite-size scaling analysis based on the KT form of the correlation length, ξαexp(c/√T/T_{KT} - 1), we determine the KT transition temperature and the decay exponent η as T_{KT} = 0.8933(6) and η = 0.243(4) for the 2D XY model. We investigate two transitions of the KT type for the 2D q-state clock models with q = 6,8,12 and confirm the prediction of η = 4/q^{2} at T_{1}, the low-temperature critical point between the ordered and XY-like phases, systematically.

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

Article number | 184405 |

Pages (from-to) | 1844051-1844055 |

Number of pages | 5 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 65 |

Issue number | 18 |

Publication status | Published - 2002 May 1 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*65*(18), 1844051-1844055. [184405].

**Probability-changing cluster algorithm for two-dimensional XY and clock models.** / Tomita, Yusuke; Okabe, Yutaka.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 65, no. 18, 184405, pp. 1844051-1844055.

}

TY - JOUR

T1 - Probability-changing cluster algorithm for two-dimensional XY and clock models

AU - Tomita, Yusuke

AU - Okabe, Yutaka

PY - 2002/5/1

Y1 - 2002/5/1

N2 - We extend the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm to the study of systems with the vector order parameter. Wolff's idea of the embedded cluster formalism is used for assigning clusters. The Kosterlitz-Thouless (KT) transitions for the two-dimensional (2D) XY and q-state clock models are studied by using the PCC algorithm. Combined with the finite-size scaling analysis based on the KT form of the correlation length, ξαexp(c/√T/TKT - 1), we determine the KT transition temperature and the decay exponent η as TKT = 0.8933(6) and η = 0.243(4) for the 2D XY model. We investigate two transitions of the KT type for the 2D q-state clock models with q = 6,8,12 and confirm the prediction of η = 4/q2 at T1, the low-temperature critical point between the ordered and XY-like phases, systematically.

AB - We extend the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm to the study of systems with the vector order parameter. Wolff's idea of the embedded cluster formalism is used for assigning clusters. The Kosterlitz-Thouless (KT) transitions for the two-dimensional (2D) XY and q-state clock models are studied by using the PCC algorithm. Combined with the finite-size scaling analysis based on the KT form of the correlation length, ξαexp(c/√T/TKT - 1), we determine the KT transition temperature and the decay exponent η as TKT = 0.8933(6) and η = 0.243(4) for the 2D XY model. We investigate two transitions of the KT type for the 2D q-state clock models with q = 6,8,12 and confirm the prediction of η = 4/q2 at T1, the low-temperature critical point between the ordered and XY-like phases, systematically.

UR - http://www.scopus.com/inward/record.url?scp=0000732855&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000732855&partnerID=8YFLogxK

M3 - Article

VL - 65

SP - 1844051

EP - 1844055

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 18

M1 - 184405

ER -