A note on Edwards' hypothesis for zero-temperature Ising dynamics

Statistical and Nonlinear Physics

Abstract.

We give a simple criterion for testing a behavior à la Edwards in certain zero-temperature, ferromagnetic spin-flip dynamics and use it to show that the limiting distributions of those dynamics do not coincide with the uniform distribution over the blocked configurations of the dynamics. We provide explicit examples in dimension one and higher.

Keywords

Spectroscopy Neural Network State Physics Complex System Uniform Distribution 

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References

  1. S.F. Edwards, in Granular Matter: An Interdisciplinary Approach, edited by A. Mehta (Springer, New York, 1994) Google Scholar
  2. S.F. Edwards, in Disorder in Condensed Matter Physics, edited by J. Blackman, J. Taguena (Oxford Univ. Press, 1991) Google Scholar
  3. A. Mehta, S.F. Edwards, Physica A 157, 1091 (1989) CrossRefGoogle Scholar
  4. H.A. Makse, J. Kurchan, Nature 415, 614 (2002) CrossRefPubMedGoogle Scholar
  5. A. Barrat, J. Kurchan, V. Loreto, M. Sellitto, Phys. Rev. Lett. 85, 5034 (2001) CrossRefGoogle Scholar
  6. A. Barrat, J. Kurchan, V. Loreto, M. Sellitto, Phys. Rev. E 63, 51301 (2001) CrossRefGoogle Scholar
  7. D.S. Dean, A. Lefèvre, Phys. Rev. Lett. 86, 5639 (2001) CrossRefPubMedGoogle Scholar
  8. A. Lefèvre, D.S. Dean, J. Phys. A 34, L213 (2001) Google Scholar
  9. D.S. Dean, A. Lefèvre, Phys. Rev. E 64, 46110 (2001) CrossRefGoogle Scholar
  10. G. De Smedt, C. Godrèche, J.M. Luck, Eur. Phys. J. B 27, 363 (2002) CrossRefGoogle Scholar
  11. C. Godrèche, J.M. Luck, e-print arXiv:cond-mat/0412077 Google Scholar
  12. D. Howard, C.M. Newman, J. Stat. Phys. 111, 57 (2003) CrossRefGoogle Scholar
  13. F. Camia, C.M. Newman, V. Sidoravicius, Comm. Math. Phys. 246, 311 (2004) CrossRefGoogle Scholar
  14. F. Camia, C.M. Newman, J. Stat. Phys. 114, 1199 (2004) CrossRefGoogle Scholar
  15. F. Camia, e-print arXiv:cond-mat/0410543 Google Scholar
  16. T.E. Harris, Proceedings of the Cambridge Phil. Soc. 56, 13 (1960) Google Scholar
  17. C.M. Fortuin, P.W. Kasteleyn, J. Ginibre, Comm. Math. Phys. 22, 89 (1971) CrossRefGoogle Scholar
  18. G.R. Grimmett, Percolation, 2nd edn. (Springer, Berlin, 1999) Google Scholar
  19. T.E. Harris, Ann. Probab. 5, 451 (1975) Google Scholar
  20. T.M. Liggett, Interacting Particle Systems (Springer, New York, 1985) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Authors and Affiliations

  1. 1.EURANDOM, P.O. Box 513EindhovenThe Netherlands

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