Fractal Configurations of the Two- and Three-Dimensional Ising Models at the Critical Point : Condensed Matter and Statistical Physics
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概要
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The fractal structure of the Ising model at the critical point T_c is studied in the present paper. The fractal dimensionality D of the total magnetization at T_c was estimated numerically as D=1.86±0.01 for the two-dimensional square lattice and D=2.46±0.01 for the three-dimensional simple cubic lattice by Monte Carlo simulations. These values agree very well with the value D=1.875 obtained from the exact critical exponents and D=2.48 obtained from the known critical exponents, respectively, through the relation D=d-β/ν=(d+γ/ν)/2. This fractalness yields the hyperscaling relation dν=2β+γ. It was also observed how the fractal nature of the relevant system disappears as the system deviates from the critical point. The dimensionality d of the relevant lattice is observed at temperatures lower than T_c and the random percolation value d/2 at higher temperatures.
- 理論物理学刊行会の論文
- 1987-06-25
著者
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SUZUKI Masatoki
Department of Physics, Rikkyo University
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Ito Nobuyasu
Institute For Theoretical Physics University Of Cologne : Hlrz At The Kfa Julich : Computing And Inf
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SUZUKI Masuo
Institute for Solid State Physics University of Tokyo
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Ito Nobuyasu
Institute Of Physics University Of Tokyo
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Suzuki Masuo
Institute Of Physics University Of Tokyo
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ITO Nobuyasu
Institute of Physics, University of Tokyo
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Suzuki Masuo
Physics Department, Saitama University
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