Cluster analysis and finite-size scaling for Ising spin systems

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.