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

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

2000-05-10

arxiv.org/abs/cond-mat/0005167v1

Physica A281, 233-241 (2000)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1016/S0378-4371(00)00034-0

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.

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