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

arXiv:cond-mat/0005167 · Physica A Statistical Mechanics and its Applications

Cluster analysis of the Ising model and universal finite-size scaling

Yutaka Okabe, Kazuhisa Kaneda, Yusuke Tomita, Macoto Kikuchi, Chin-Kun Hu

Published Jun 1, 2000• 2 citations
arXivHTMLPDF
DOI
10.1016/s0378-4371(00)00034-0

Related papers

Universal amplitude ratios in finite-size scaling: three-dimensional Ising model

Martin Weigel

Nuclear Physics B - Proceedings Supplements•Mar 1, 2000•0 citations

Universal amplitude ratios in finite-size scaling: three-dimensional Ising model

Martin Weigel, Wolfhard Janke

arXiv:cond-mat/0009032•Nuclear Physics B - Proceedings Supplements•Apr 1, 2000•1 citation

Clusters and Critical Behavior in the Ising Model

Jean-Luc Cambier

•Jan 1, 1985•0 citations

Cluster Analysis of the Ising Model and Universal Finite-Size Scaling

Yutaka Okabe, Kazuhisa Kaneda, Yusuke Tomita +2 more

The recent progress in the study of finite-size scaling (FSS) properties of the Ising model is briefly reviewed. We calculate the universal FSS functions for the Binder parameter g and the magnetization distribution function p(m) for the Ising model on L1×L2 two-dimensional lattices with tilted boundary conditions. We show that the FSS functions are universal for fixed sets of the aspect ratio L1/L2 and the tilt parameter. We also study the percolating properties of the Ising model, giving attention to the effects of the aspect ratio of finite systems. We elucidate the origin of the complex structure of p(m) for the system with large aspect ratio by the multiple-percolating-cluster argument.

•Jan 1, 2000•2 citations

The Finite-Size Scaling Study of Five-Dimensional Ising Model

Ziya Merdan, Nida Aras, Cihan Kürkçü

Acta Physica Polonica A•Jun 1, 2016•0 citations

Cluster analysis and finite-size scaling for Ising spin systems

Yusuke Tomita, Yutaka Okabe, Chin‐Kun Hu

Based on the connection between the Ising model and a correlated percolation model, we calculate the distribution function for the fraction (c) of lattice sites in percolating clusters in subgraphs with n percolating clusters, f(n)(c), and the distribution function for magnetization (m) in subgraphs with n percolating clusters, p(n)(m). We find that f(n)(c) and p(n)(m) have very good finite-size scaling behavior and that they have universal finite-size scaling functions for the model on square, plane triangular, and honeycomb lattices when aspect ratios of these lattices have the proportions 1:square root[3]/2:square root[3]. The complex structure of the magnetization distribution function p(m) for the system with large aspect ratio could be understood from the independent orientations of two or more percolation clusters in such a system.

arXiv:cond-mat/9907076•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Sep 1, 1999•39 citations
The recent progress in the study of finite-size scaling (FSS) properties of the Ising model is briefly reviewed. We calculate the universal FSS functions for the Binder parameter g and the magnetization distribution function p(m) for the Ising model on L1×L2 two-dimensional lattices with tilted boundary conditions. We show that the FSS functions are universal for fixed sets of the aspect ratio L1/L2 and the tilt parameter. We also study the percolating properties of the Ising model, giving attention to the effects of the aspect ratio of finite systems. We elucidate the origin of the complex structure of p(m) for the system with large aspect ratio by the multiple-percolating-cluster argument.
Based on the connection between the Ising model and a correlated percolation model, we calculate the distribution function for the fraction (c) of lattice sites in percolating clusters in subgraphs with n percolating clusters, f(n)(c), and the distribution function for magnetization (m) in subgraphs with n percolating clusters, p(n)(m). We find that f(n)(c) and p(n)(m) have very good finite-size scaling behavior and that they have universal finite-size scaling functions for the model on square, plane triangular, and honeycomb lattices when aspect ratios of these lattices have the proportions 1:square root[3]/2:square root[3]. The complex structure of the magnetization distribution function p(m) for the system with large aspect ratio could be understood from the independent orientations of two or more percolation clusters in such a system.