Cluster Analysis and Finite-Size Scaling for Ising Spin Systems

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 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:$\sqrt{3}$/2:$\sqrt{3}$. 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 system.

5 pages including 10 eps figures, RevTeX, to appear in Phys. Rev. E

References in corpus (1)

• The Number of Incipient Spanning Clusters in Two-Dimensional Percolation

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