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Precision calculation of elasticity for percolation

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Abstract

Monte Carlo transfer matrix evaluation of the elastic constants at the percolation threshold of the random-bond honeycomb lattice, with widths of up to 96 and lengths of about two million lattice constants (roughly 200 hours CDC Cyber 205 vector computer time) gave a critical exponentT=3.96±0.04 with a logarithmic correction term. This exponent agrees well with the scaling hypothesisT=t+2v=3.97, relatingT to the two-dimensional conductivity exponent.

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Authors and Affiliations

  1. Supercomputer Institute, University of Minnesota, 55455, Minneapolis, Minesota, USA

    J. G. Zabolitzky

  2. School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Ramat Aviv, Israel

    D. J. Bergman

  3. Institute of Theoretical Physics, Cologne University, 5000, Köln 41, West Germany

    D. Stauffer

Authors
  1. J. G. Zabolitzky
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  2. D. J. Bergman
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  3. D. Stauffer
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Additional information

We thank G. Güntherodt, B. I. Halperin, B. Hillebrands, and S. Roux for discussions, and the SFB 125 for support. This research was supported at Tel Aviv University in part by a grant from The Israel Academy of Sciences.

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Zabolitzky, J.G., Bergman, D.J. & Stauffer, D. Precision calculation of elasticity for percolation. J Stat Phys 44, 211–223 (1986). https://doi.org/10.1007/BF01010913

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  • DOI: https://doi.org/10.1007/BF01010913

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