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Cluster Analysis and Finite-Size Scaling for Ising Spin Systems | | Yusuke Tomita
; Yutaka Okabe
; Chin-Kun Hu
; | | Date: |
6 Jul 1999 | | Journal: | Phys. Rev. E60, 2716-2720 (1999) | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | 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. | | Source: | arXiv, cond-mat/9907076 | | Services: | Forum | Review | PDF | Favorites | |
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