Abstract
Based on the connection between the Ising model and a correlated percolation model, we calculate the distribution function for the fraction of lattice sites in percolating clusters in subgraphs with n percolating clusters, and the distribution function for magnetization in subgraphs with n percolating clusters, We find that and 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 The complex structure of the magnetization distribution function for the system with large aspect ratio could be understood from the independent orientations of two or more percolation clusters in such a system.
- Received 25 November 1998
DOI:https://doi.org/10.1103/PhysRevE.60.2716
©1999 American Physical Society