# Novel Monte Carlo algorithms and their applications

Yutaka Okabe, Yusuke Tomita, Chiaki Yamaguchi

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

We describe a generalized scheme for the probability-changing cluster (PCC) algorithm, based on the study of the finite-size scaling property of the correlation ratio, the ratio of the correlation functions with different distances. We apply this generalized PCC algorithm to the two-dimensional 6-state clock model. We also discuss the combination of the cluster algorithm and the extended ensemble method. We derive a rigorous broad histogram relation for the bond number. A Monte Carlo dynamics based on the number of potential moves for the bond number is proposed, and applied to the three-dimensional Ising and 3-state Potts models.

Original language English 340-350 11 Physica A: Statistical Mechanics and its Applications 321 1-2 https://doi.org/10.1016/S0378-4371(02)01792-2 Published - 2003 Apr 1 Yes

Bond number
histograms
clocks
scaling

### Keywords

• Cluster algorithm
• Correlation ratio
• Finite-size scaling

### ASJC Scopus subject areas

• Mathematical Physics
• Statistical and Nonlinear Physics

### Cite this

Novel Monte Carlo algorithms and their applications. / Okabe, Yutaka; Tomita, Yusuke; Yamaguchi, Chiaki.

In: Physica A: Statistical Mechanics and its Applications, Vol. 321, No. 1-2, 01.04.2003, p. 340-350.

Research output: Contribution to journalArticle

Okabe, Yutaka ; Tomita, Yusuke ; Yamaguchi, Chiaki. / Novel Monte Carlo algorithms and their applications. In: Physica A: Statistical Mechanics and its Applications. 2003 ; Vol. 321, No. 1-2. pp. 340-350.
title = "Novel Monte Carlo algorithms and their applications",
abstract = "We describe a generalized scheme for the probability-changing cluster (PCC) algorithm, based on the study of the finite-size scaling property of the correlation ratio, the ratio of the correlation functions with different distances. We apply this generalized PCC algorithm to the two-dimensional 6-state clock model. We also discuss the combination of the cluster algorithm and the extended ensemble method. We derive a rigorous broad histogram relation for the bond number. A Monte Carlo dynamics based on the number of potential moves for the bond number is proposed, and applied to the three-dimensional Ising and 3-state Potts models.",
keywords = "Broad histogram relation, Cluster algorithm, Correlation ratio, Finite-size scaling",
author = "Yutaka Okabe and Yusuke Tomita and Chiaki Yamaguchi",
year = "2003",
month = "4",
day = "1",
doi = "10.1016/S0378-4371(02)01792-2",
language = "English",
volume = "321",
pages = "340--350",
journal = "Physica A: Statistical Mechanics and its Applications",
issn = "0378-4371",
publisher = "Elsevier",
number = "1-2",

}

TY - JOUR

T1 - Novel Monte Carlo algorithms and their applications

AU - Okabe, Yutaka

AU - Tomita, Yusuke

AU - Yamaguchi, Chiaki

PY - 2003/4/1

Y1 - 2003/4/1

N2 - We describe a generalized scheme for the probability-changing cluster (PCC) algorithm, based on the study of the finite-size scaling property of the correlation ratio, the ratio of the correlation functions with different distances. We apply this generalized PCC algorithm to the two-dimensional 6-state clock model. We also discuss the combination of the cluster algorithm and the extended ensemble method. We derive a rigorous broad histogram relation for the bond number. A Monte Carlo dynamics based on the number of potential moves for the bond number is proposed, and applied to the three-dimensional Ising and 3-state Potts models.

AB - We describe a generalized scheme for the probability-changing cluster (PCC) algorithm, based on the study of the finite-size scaling property of the correlation ratio, the ratio of the correlation functions with different distances. We apply this generalized PCC algorithm to the two-dimensional 6-state clock model. We also discuss the combination of the cluster algorithm and the extended ensemble method. We derive a rigorous broad histogram relation for the bond number. A Monte Carlo dynamics based on the number of potential moves for the bond number is proposed, and applied to the three-dimensional Ising and 3-state Potts models.

KW - Cluster algorithm

KW - Correlation ratio

KW - Finite-size scaling

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M3 - Article

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VL - 321

SP - 340

EP - 350

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

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