### Abstract

Based on the connection between the Ising model and a correlated percolation model, we calculate the distribution function for the fraction [Formula Presented] of lattice sites in percolating clusters in subgraphs with n percolating clusters, [Formula Presented] and the distribution function for magnetization [Formula Presented] in subgraphs with n percolating clusters, [Formula Presented] We find that [Formula Presented] and [Formula Presented] 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 [Formula Presented] The complex structure of the magnetization distribution function [Formula Presented] 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 |
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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 |

DOIs | |

Publication status | Published - 1999 Jan 1 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

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

*60*(3), 2716-2720. https://doi.org/10.1103/PhysRevE.60.2716