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Proposed connection between critical exponents and fractal dimensions in the Ising model

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Abstract

Scaling properties near the critical point indicates the existence of self-similarity behavior for the critical phenomena. Although the system considered here is not a truly dynamic one, we propose a specific set of relations between fractal dimensions and critical exponents in the Ising model of statistical mechanics. In particular, we put forward, corresponding to six critical exponents for the Ising model, six fractal dimensions. Assuming the latter proposals, we can then derive relationships between such fractal dimensions.

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Authors and Affiliations

  1. Shenyang National Laboratory for Materials Science, Institute of Metal Research and International Centre for Materials Physics, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang, 110016, People’s Republic of China

    Z. D. Zhang

  2. Department of Physics, University of Antwerp, Antwerp, Belgium

    N. H. March

  3. Oxford University, Oxford, UK

    N. H. March

Authors
  1. Z. D. Zhang
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  2. N. H. March
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Correspondence to Z. D. Zhang.

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Zhang, Z.D., March, N.H. Proposed connection between critical exponents and fractal dimensions in the Ising model. J Math Chem 50, 920–925 (2012). https://doi.org/10.1007/s10910-011-9935-z

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  • DOI: https://doi.org/10.1007/s10910-011-9935-z

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