### 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 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 language | English |
---|---|

Pages (from-to) | 2716-2720 |

Number of pages | 5 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 60 |

Issue number | 3 |

Publication status | Published - 1999 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*60*(3), 2716-2720.

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

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 60, no. 3, pp. 2716-2720.

}

TY - JOUR

T1 - Cluster analysis and finite-size scaling for Ising spin systems

AU - Tomita, Yusuke

AU - Okabe, Yutaka

AU - Hu, Chin Kun

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0001034801&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001034801&partnerID=8YFLogxK

M3 - Article

C2 - 11970074

AN - SCOPUS:0001034801

VL - 60

SP - 2716

EP - 2720

JO - Physical review. E

JF - Physical review. E

SN - 1539-3755

IS - 3

ER -