Cluster analysis and finite-size scaling for Ising spin systems

Yusuke Tomita, Yutaka Okabe, Chin Kun Hu

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

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, fn(c), and the distribution function for magnetization (m) in subgraphs with n percolating clusters, pn(m). We find that fn(c) and pn(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:√3/2:√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.

Original languageEnglish
Pages (from-to)2716-2720
Number of pages5
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume60
Issue number3
Publication statusPublished - 1999
Externally publishedYes

Fingerprint

cluster analysis
scaling
distribution functions
aspect ratio
magnetization
Ising model
proportion

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Cluster analysis and finite-size scaling for Ising spin systems. / Tomita, Yusuke; Okabe, Yutaka; Hu, Chin Kun.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 60, No. 3, 1999, p. 2716-2720.

Research output: Contribution to journalArticle

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