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Cluster Analysis and Finite-Size Scaling for Ising Spin Systems

Authors
  • Tomita, Yusuke
  • Okabe, Yutaka
  • Hu, Chin-Kun
Type
Published Article
Publication Date
Jul 06, 1999
Submission Date
Jul 06, 1999
Identifiers
DOI: 10.1103/PhysRevE.60.2716
arXiv ID: cond-mat/9907076
Source
arXiv
License
Unknown
External links

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, $f_n(c)$, 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 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:$\sqrt 3$/2:$\sqrt 3$. 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 system.

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