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

Yusuke Tomita, Yutaka Okabe

Research output: Contribution to journalArticle

52 Citations (Scopus)

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/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.

Original languageEnglish
Article number184405
Pages (from-to)1844051-1844055
Number of pages5
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume65
Issue number18
Publication statusPublished - 2002 May 1
Externally publishedYes

Fingerprint

clocks
Clocks
Superconducting transition temperature
critical point
transition temperature
exponents
formalism
scaling
decay
predictions
Temperature
tokaratoxin 1

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

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

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 65, No. 18, 184405, 01.05.2002, p. 1844051-1844055.

Research output: Contribution to journalArticle

@article{d92461ba1afd404daa764eba208e9677,
title = "Probability-changing cluster algorithm for two-dimensional XY and clock models",
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/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.",
author = "Yusuke Tomita and Yutaka Okabe",
year = "2002",
month = "5",
day = "1",
language = "English",
volume = "65",
pages = "1844051--1844055",
journal = "Physical Review B-Condensed Matter",
issn = "0163-1829",
publisher = "American Institute of Physics Publising LLC",
number = "18",

}

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 -