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Prog. Theor. Phys. Vol. 69 No. 1 (1983) pp. 65-76

Phase Transition and Fractals

Masuo Suzuki

Department of Physics, University of Tokyo, Tokyo 113

(Received August 19, 1982)

Abstract:

A geometrical interpretation of critical phenomena, particularly of the scaling relations on critical exponents is given by the use of statistical fractal dimensionality. The relation between this geometrical interpretation and the finite size scaling theory is also discussed.
The concept of connectivity dimensionality (or generalized fractal topological dimensionality) is introduced to discuss the relation between critical exponents and fractal dimensionalities of some explicit lattices.

URL : http://ptp.ipap.jp/link?PTP/69/65/
DOI : 10.1143/PTP.69.65

[ Full Text PDF : FREE ACCESS (501K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

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6. The content of the present paper has been partly reported in a domestic journal "Mathematical Science" No. 221, November (1981), 13, in Japanese.
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    See also, B. Sutherland, Phys. Rev. Lett. 18 (1974), 279[APS]; W. F. Wreszinski, Nuovo Cim. B 33 (1976), 591.
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Citing Article(s) :

1. Journal of the Physical Society of Japan 57 (1988) pp. 2585-2587 :

   Fractal Clusters and Stable Distribution

   Hideki Takayasu

2. Journal of the Physical Society of Japan 58 (1989) pp. 1962-1967 :

   A Model for Phase Transition on Sierpinski Gaskets

   Takayuki Abe

3. Journal of the Physical Society of Japan 58 (1989) pp. 3642-3650 :

   Canonical Series of Exactly Solvable Models for the CAM –Spontaneous Broken Symmetry of Effective Hamiltonians Based on the Confluent Transfer-Matrix Method–

   Masuo Suzuki

4. Journal of the Physical Society of Japan 73 (2004) pp. 3299-3303 :

   Spontaneous Symmetry Breaking by Local or Partial Fields

   Masuo Suzuki and Hidenori Suzuki

5. Progress of Theoretical Physics Vol. 71 No. 6 (1984) pp. 1397-1400 :

   Finite-Size Scaling for Transient Similarity and Fractals

   Masuo Suzuki

6. Progress of Theoretical Physics Vol. 74 No. 4 (1985) pp. 916-917 :

   Scaling Theory of Potts Model and Fractal Dimensions

   Mamoru Yamashita

7. Progress of Theoretical Physics Vol. 77 No. 6 (1987) pp. 1391-1401 :

   Fractal Configurations of the Two- and Three-Dimensional Ising Models at the Critical Point

   Nobuyasu Ito and Masuo Suzuki

8. Progress of Theoretical Physics Vol. 79 No. 5 (1988) pp. 1080-1094 :

   Percolation Problem Describing ±J Ising Spin Glass System

   Yasuhiro Kasai and Ayao Okiji

9. Progress of Theoretical Physics Vol. 79 No. 6 (1988) pp. 1330-1344 :

   Asymptotic Behaviour of Density and Correlation in Diffusion-Limited Reactions A + B →0 and A + A →0

   Shokichi Kanno

10. Progress of Theoretical Physics Supplement No.79 (1984) pp. 125-140 :

    Fluctuation and Formation of Macroscopic Order in Non-Equilibrium Systems

    Masuo Suzuki

11. Progress of Theoretical Physics Supplement No.114 (1993) pp. 1-17 :

    Analytic Study of Fractal Structure of Quantized Surface in Two-Dimensional Quantum Gravity

    Yoshiyuki Watabiki

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