Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the American Physical Society

Critical nonequilibrium relaxation in cluster algorithms using the Binder ratio and its application to bond-diluted Ising models

Yoshihiko Nonomura, Yusuke Tomita

Published Mar 17, 2017• 0 citations
OpenAlex

Related papers

Critical dynamics of cluster algorithms in the dilute Ising model

Michael Hennecke, U. Heyken

Journal of Statistical Physics•Aug 1, 1993•12 citations

Critical nonequilibrium relaxation in cluster-update quantum Monte Carlo algorithms and its application to quantum phase transitions

Yoshihiko Nonomura, Yusuke Tomita

Bulletin of the American Physical Society•Mar 5, 2018•0 citations

Monte Carlo analysis of the critical properties of the two-dimensional randomly bond-diluted Ising model via Wang–Landau algorithm

Ioannis A. Hadjiagapiou

Physica A Statistical Mechanics and its Applications•Dec 22, 2010•16 citations

Cluster nonequilibrium relaxation in Ising models observed with the Binder ratio

Yoshihiko Nonomura, Yusuke Tomita

The Binder ratios exhibit discrepancy from the Gaussian behavior of the magnetic cumulants, and their size independence at the critical point has been widely utilized in numerical studies of critical phenomena. In the present article we reformulate the nonequilibrium relaxation (NER) analysis in cluster algorithms using the $(2,1)$-Binder ratio, and apply this scheme to the two- and three-dimensional Ising models. Although the stretched-exponential relaxation behavior at the critical point is not explicitly observed in this quantity, we find that there exists a logarithmic finite-size scaling formula which can be related with a similar formula recently derived in cluster NER of the correlation length, and that the formula enables precise evaluation of the critical point and the stretched-exponential relaxation exponent $σ$. Physical background of this novel behavior is explained by the simulation-time dependence of the distribution function of magnetization in two dimensions and temperature dependence of $σ$ obtained from magnetization in three dimensions.

arXiv:1801.10315•Jan 31, 2018•0 citations

Nontrivial nonequilibrium critical relaxation in cluster algorithms and universal nonequilibrium-to-equilibrium scaling procedure

Yoshihiko Nonomura, Yusuke Tomita

Bulletin of the American Physical Society•Mar 2, 2015•0 citations

Crossover and self-averaging in the two-dimensional site-diluted Ising model: Application of probability-changing cluster algorithm

Yusuke Tomita, Yutaka Okabe

Using the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since we can tune the critical point of each random sample automatically with the PCC algorithm, we succeed in studying the sample-dependent T(c)(L) and the sample average of physical quantities at each T(c)(L) systematically. Using the finite-size scaling (FSS) analysis for T(c)(L), we discuss the importance of corrections to FSS both in the strong-dilution and weak-dilution regions. The critical phenomena of the 2D site-diluted Ising model are shown to be controlled by the pure fixed point. The crossover from the percolation fixed point to the pure Ising fixed point with the system size is explicitly demonstrated by the study of the Binder parameter. We also study the distribution of critical temperature T(c)(L). Its variance shows the power-law L dependence, L(-n), and the estimate of the exponent n is consistent with the prediction of Aharony and Harris [Phys. Rev. Lett. 77, 3700 (1996)]. Calculating the relative variance of critical magnetization at the sample-dependent T(c)(L), we show that the 2D site-diluted Ising model exhibits weak self-averaging.

arXiv:cond-mat/0106154•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Aug 27, 2001•32 citations
The Binder ratios exhibit discrepancy from the Gaussian behavior of the magnetic cumulants, and their size independence at the critical point has been widely utilized in numerical studies of critical phenomena. In the present article we reformulate the nonequilibrium relaxation (NER) analysis in cluster algorithms using the (2,1)(2,1)(2,1)-Binder ratio, and apply this scheme to the two- and three-dimensional Ising models. Although the stretched-exponential relaxation behavior at the critical point is not explicitly observed in this quantity, we find that there exists a logarithmic finite-size scaling formula which can be related with a similar formula recently derived in cluster NER of the correlation length, and that the formula enables precise evaluation of the critical point and the stretched-exponential relaxation exponent σσσ. Physical background of this novel behavior is explained by the simulation-time dependence of the distribution function of magnetization in two dimensions and temperature dependence of σσσ obtained from magnetization in three dimensions.
Using the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since we can tune the critical point of each random sample automatically with the PCC algorithm, we succeed in studying the sample-dependent T(c)(L) and the sample average of physical quantities at each T(c)(L) systematically. Using the finite-size scaling (FSS) analysis for T(c)(L), we discuss the importance of corrections to FSS both in the strong-dilution and weak-dilution regions. The critical phenomena of the 2D site-diluted Ising model are shown to be controlled by the pure fixed point. The crossover from the percolation fixed point to the pure Ising fixed point with the system size is explicitly demonstrated by the study of the Binder parameter. We also study the distribution of critical temperature T(c)(L). Its variance shows the power-law L dependence, L(-n), and the estimate of the exponent n is consistent with the prediction of Aharony and Harris [Phys. Rev. Lett. 77, 3700 (1996)]. Calculating the relative variance of critical magnetization at the sample-dependent T(c)(L), we show that the 2D site-diluted Ising model exhibits weak self-averaging.