Cluster Analysis of the Ising Model and Universal Finite-Size Scaling

Yutaka Okabe; Kazuhisa Kaneda; Yusuke Tomita; Macoto Kikuchi; Chin-Kun Hu

doi:10.1016/S0378-4371(00)00034-0

paper

Cluster Analysis of the Ising Model and Universal Finite-Size Scaling

arXiv:cond-mat/0005167 · doi:10.1016/S0378-4371(00)00034-0

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 $L_{1} \times L_{2}$ 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.

11 pages including 6 eps figures, elsart.sty, to appear in Physica A