Critical nonequilibrium cluster-flip relaxations in Ising models

Yusuke Tomita, Yoshihiko Nonomura

Research output: Contribution to journalArticle

Abstract

We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the stretched-exponential function, we find that the dynamics changes from the stretched exponential to the power function as the dimensionality is increased: The two-, three-, four-, and infinite-dimensional Ising models are numerically studied, and the four- and infinite-dimensional Ising models exhibit the power-law relaxation. We also show that the finite-size scaling analysis using the normalized correlation length is markedly effective for the analysis of relaxational processes rather than the direct use of the Monte Carlo step.

Original languageEnglish
Article number052110
JournalPhysical Review E
Volume98
Issue number5
DOIs
Publication statusPublished - 2018 Nov 12

Fingerprint

Ising model
critical point
exponential functions
scaling

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Critical nonequilibrium cluster-flip relaxations in Ising models. / Tomita, Yusuke; Nonomura, Yoshihiko.

In: Physical Review E, Vol. 98, No. 5, 052110, 12.11.2018.

Research output: Contribution to journalArticle

@article{e91b34a36ba64296a13566f9a45a5bc7,
title = "Critical nonequilibrium cluster-flip relaxations in Ising models",
abstract = "We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the stretched-exponential function, we find that the dynamics changes from the stretched exponential to the power function as the dimensionality is increased: The two-, three-, four-, and infinite-dimensional Ising models are numerically studied, and the four- and infinite-dimensional Ising models exhibit the power-law relaxation. We also show that the finite-size scaling analysis using the normalized correlation length is markedly effective for the analysis of relaxational processes rather than the direct use of the Monte Carlo step.",
author = "Yusuke Tomita and Yoshihiko Nonomura",
year = "2018",
month = "11",
day = "12",
doi = "10.1103/PhysRevE.98.052110",
language = "English",
volume = "98",
journal = "Physical review. E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "5",

}

TY - JOUR

T1 - Critical nonequilibrium cluster-flip relaxations in Ising models

AU - Tomita, Yusuke

AU - Nonomura, Yoshihiko

PY - 2018/11/12

Y1 - 2018/11/12

N2 - We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the stretched-exponential function, we find that the dynamics changes from the stretched exponential to the power function as the dimensionality is increased: The two-, three-, four-, and infinite-dimensional Ising models are numerically studied, and the four- and infinite-dimensional Ising models exhibit the power-law relaxation. We also show that the finite-size scaling analysis using the normalized correlation length is markedly effective for the analysis of relaxational processes rather than the direct use of the Monte Carlo step.

AB - We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the stretched-exponential function, we find that the dynamics changes from the stretched exponential to the power function as the dimensionality is increased: The two-, three-, four-, and infinite-dimensional Ising models are numerically studied, and the four- and infinite-dimensional Ising models exhibit the power-law relaxation. We also show that the finite-size scaling analysis using the normalized correlation length is markedly effective for the analysis of relaxational processes rather than the direct use of the Monte Carlo step.

UR - http://www.scopus.com/inward/record.url?scp=85056671838&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056671838&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.98.052110

DO - 10.1103/PhysRevE.98.052110

M3 - Article

AN - SCOPUS:85056671838

VL - 98

JO - Physical review. E

JF - Physical review. E

SN - 1539-3755

IS - 5

M1 - 052110

ER -