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Scaling Relations for Two-Dimensional Ising Percolation

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Abstract

We consider the percolation problem in the high-temperature Ising model on the two-dimensional square lattice at or near critical external fields. We show that all scaling relations, except for a single hyperscaling relation, hold under the power law assumptions for the one-arm path and the four-arm paths.

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Acknowledgements

The third author would like to thank the hospitality of Kobe University and Osaka Electro-Communication University. Part of the work done when he visited there.

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Authors and Affiliations

  1. Department of Mathematics, Kobe University, 1-1 Rokko, Kobe, 657-8501, Japan

    Yasunari Higuchi

  2. Department of Engineering Science, Osaka Electro-Communication University, Neyagawa, Osaka, 572-8530, Japan

    Masato Takei

  3. Department of Mathematics, University of Colorado, Colorado Springs, CO, 80933, USA

    Yu Zhang

Authors
  1. Yasunari Higuchi
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  2. Masato Takei
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  3. Yu Zhang
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Corresponding author

Correspondence to Masato Takei.

Additional information

Supported by JSPS Grant-in-Aid for Scientific Research (A) No. 22244007 (Y.H.) and by JSPS Grant-in-Aid for Young Scientists (B) No. 21740087 (M.T.).

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Higuchi, Y., Takei, M. & Zhang, Y. Scaling Relations for Two-Dimensional Ising Percolation. J Stat Phys 148, 777–799 (2012). https://doi.org/10.1007/s10955-012-0561-3

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  • DOI: https://doi.org/10.1007/s10955-012-0561-3

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