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Cluster Analysis of the Ising Model and Universal Finite-Size Scaling | | Yutaka Okabe
; Kazuhisa Kaneda
; Yusuke Tomita
; Macoto Kikuchi
; Chin-Kun Hu
; | | Date: |
10 May 2000 | | Journal: | Physica A281, 233-241 (2000) | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Abstract: | The recent progress in the study of finite-size scaling (FSS) properties of the Ising model is briefly reviewed. We calculate the universal FSS functions for the Binder parameter $g$ and the magnetization distribution function $p(m)$ for the Ising model on $L_1 imes L_2$ two-dimensional lattices with tilted boundary conditions. We show that the FSS functions are universal for fixed sets of the aspect ratio $L_1/L_2$ and the tilt parameter. We also study the percolating properties of the Ising model, giving attention to the effects of the aspect ratio of finite systems. We elucidate the origin of the complex structure of $p(m)$ for the system with large aspect ratio by the multiple-percolating-cluster argument. | | Source: | arXiv, cond-mat/0005167 | | Services: | Forum | Review | PDF | Favorites | |
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