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On the ground-state threshold in random two-dimensional Ising ±J models

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Abstract

For square, triangular, and for hexagonal lattices there is numerical and theoretical support that the ground-state thresholdp c between ferro- and paramagnetism in random 2D Ising ±J models, withp as the concentration of antiferromagnetic bonds, is identical top *which is characterized by minimal matching properties of frustrated plaquettes. From square lattices of size 100×100 we have got pc,sq<0.117 by simulations which produced average groundstate magnetizations per spin by means of exact minimal matchings. Moreover, from the squareL×L-lattices treated (L = 10, 20, 50, 100) we obtained the estimatep c,sq ≈0.1 which is in agreement with the Grinstein estimatep c,sq ≈0.099 andp c,sq ≈0.105 by Freund and Grassberger.

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References

  1. M. Achilles, J. Bendisch, K. Cassirer, and H. von Trotha, GMD-Studies No. 186, Gesellschaft für Mathematik und Datenverarbeitung, D-5205 St. Augustin, Germany (1991).

  2. F. Barahona, R. Maynard, R. Rammal, and J. P. Uhry,J. Phys.: Math. Gen. 15:673 (1982).

    Google Scholar 

  3. J. Bendisch,J. Stat. Phys. 62:435 (1991).

    Google Scholar 

  4. I. Bieche, R. Maynard, R. Rammal, and J. P. Uhry,J. Phys. A: Math. Gen. 13:2553 (1980).

    Google Scholar 

  5. U. Derigs and A. Metz,Mathematical Programming 50:113 (1991).

    Google Scholar 

  6. H. Freund and P. Grassberger,J. Phys. A: Math. Gen. 22:4045 (1989).

    Google Scholar 

  7. G. Grinstein, C. Jayaprakash, and M. Wortis,Phys. Rev. B 19:260 (1979).

    Google Scholar 

  8. S. Kirkpatrick,Phys. Rev. B 16:4630 (1977).

    Google Scholar 

  9. I. Morgenstern and K. Binder,Phys. Rev. B 22:288 (1980).

    Google Scholar 

  10. I. Ono,J. Phys. Soc. Jpn. 41:345 (1976).

    Google Scholar 

  11. G. Toulouse,Commun. Phys. 2:115 (1977).

    Google Scholar 

  12. J. Vannimenu and G. Toulouse,J. Phys. C 10:L537 (1977).

    Google Scholar 

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  1. Gesellschaft für Mathematik und Datenverarbeitung, D-5205, Sankt Augustin, Germany

    J. Bendisch

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  1. J. Bendisch
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Bendisch, J. On the ground-state threshold in random two-dimensional Ising ±J models. J Stat Phys 67, 1209–1217 (1992). https://doi.org/10.1007/BF01049016

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  • DOI: https://doi.org/10.1007/BF01049016

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