Cluster analysis and finite-size scaling for Ising spin systems

Based on the connection between the Ising model and a correlated percolatio n model, we calculate the distribution function for the fraction (c) of lat tice sites in percolating clusters in subgraphs with n percolating clusters , f(n)(c), and the distribution function for magnetization (rn) in subgraph s with n percolating clusters, p(n)(m). We find that f(n)(c) and p(n)(m) ha ve very good finite-size scaling behavior and that they have universal fini te-size scaling functions for the model on square,plane triangular, and hon eycomb lattices when aspect ratios of these lattices have the proportions 1 :root 3/2:root 3. The complex structure of the magnetization distribution f unction p(m) for the system with large aspect ratio could be understood fro m the independent orientations of two or more percolation clusters in such a system. [S1063-651X(99)09609-9].