Cluster Analysis and Finite-Size Scaling for Ising Spin Systems

Details Cluster Analysis and Finite-Size Scaling for Ising Spin Systems Cluster Analysis and Finite-Size Scaling for Ising Spin Systems

1999-07-06

arxiv.org/abs/cond-mat/9907076v1

Phys. Rev. E60, 2716-2720 (1999)

Physics

Condensed Matter

Statistical Mechanics

5 pages including 10 eps figures, RevTeX, to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.60.2716

Based on the connection between the Ising model and a correlated percolation model, we calculate the distribution function for the fraction ($c$) of lattice sites in percolating clusters in subgraphs with $n$ percolating clusters, $f_n(c)$, and the distribution function for magnetization ($m$) in subgraphs with $n$ percolating clusters, $p_n(m)$. We find that $f_n(c)$ and $p_n(m)$ have very good finite-size scaling behavior and they have universal finite-size scaling functions for the model on square, plane triangular, and honeycomb lattices when aspect ratios of these lattices have the proportions 1:$\sqrt 3$/2:$\sqrt 3$. The complex structure of the magnetization distribution function $p(m)$ for the system with large aspect ratio could be understood from the independent orientations of two or more percolation clusters in such system.

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