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 L1 × L2 two-dimensional lattices with titled boundary conditions. We show that the FSS functions are universal for fixed sets of the aspect ratio L1/L2 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.
| Original language | English |
|---|---|
| Pages (from-to) | 233-241 |
| Number of pages | 9 |
| Journal | Physica A: Statistical Mechanics and its Applications |
| Volume | 281 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2000 Jun 15 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mathematical Physics
- Statistical and Nonlinear Physics
Cite this
Cluster analysis of the Ising model and universal finite-size scaling. / Okabe, Yutaka; Kaneda, Kazuhisa; Tomita, Yusuke; Kikuchi, MacOto; Hu, Chin Kun.
In: Physica A: Statistical Mechanics and its Applications, Vol. 281, No. 1, 15.06.2000, p. 233-241.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Cluster analysis of the Ising model and universal finite-size scaling
AU - Okabe, Yutaka
AU - Kaneda, Kazuhisa
AU - Tomita, Yusuke
AU - Kikuchi, MacOto
AU - Hu, Chin Kun
PY - 2000/6/15
Y1 - 2000/6/15
N2 - 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 L1 × L2 two-dimensional lattices with titled boundary conditions. We show that the FSS functions are universal for fixed sets of the aspect ratio L1/L2 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.
AB - 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 L1 × L2 two-dimensional lattices with titled boundary conditions. We show that the FSS functions are universal for fixed sets of the aspect ratio L1/L2 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=0033686366&partnerID=8YFLogxK
U2 - 10.1016/S0378-4371(00)00034-0
DO - 10.1016/S0378-4371(00)00034-0
M3 - Article
VL - 281
SP - 233
EP - 241
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
SN - 0378-4371
IS - 1
ER -