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
N1 - Funding Information:
We would like to thank T. Kawakatsu, N. Hatano and N. Kawashima for valuable discussions, and the Supercomputer Center of the ISSP, University of Tokyo, for providing the computing facilities. This work was supported by a Grant-in-aid for Scientific Research from the Ministry of Education, Science, Sports and Culture, Japan and by the National Science Council of the Republic of China (Taiwan) under Grant Numbers NSC 89-2112-M-001-005.
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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U2 - 10.1016/S0378-4371(00)00034-0
DO - 10.1016/S0378-4371(00)00034-0
M3 - Conference article
AN - SCOPUS:0033686366
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
T2 - 5th Taiwan International Symposium on Statistical Physics (StatPhys-Taiwan-1999)
Y2 - 9 August 1999 through 12 August 1999
ER -