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Dynamics of Automata, Spin Glasses and Neural Network Models

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Book cover Nonlinear Evolution and Chaotic Phenomena

Part of the book series: NATO ASI Series ((NSSB,volume 176))

Abstract

These lectures describe a few dynamical properties of some statistical mechanics systems such as spin models, automata, neural networks. Two aspects will be mostly discussed: the multivalley structure of phase space (sections II, IV, V, VI, VII, VIII) and the distance between two configurations which evolve according to the same rules (sections III, IX, X).

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References

  1. K. Binder, Applications of the Monte Carlo Method in Statistical Physics (Berlin: Springer Verlag) (1984).

    MATH  Google Scholar 

  2. J.F. Fontanari and R. Köberle, preprint (1986).

    Google Scholar 

  3. E. Bienenstock, F. Fogelman Soulié and G. Weisbuch, Disordered Systems and biological organistation (Springer Verlag, Heidelberg) (1986).

    Google Scholar 

  4. S.A. Kauffman, J. Theor. Biol. 22, 437 (1969); 44, 167 (1974).

    Article  MathSciNet  Google Scholar 

  5. S.A. Kauffmari, Math. Life Sci. 3, 63 (1970).

    Google Scholar 

  6. A.E. Gelfand and C.C. Walker, Ensemble Modelling (M. Dekker) (1984).

    Google Scholar 

  7. H. Flyvbjerg and N.J. Kjaer, preprint (1987), submitted J. Phys. A.

    Google Scholar 

  8. H.J. Hilhorst and M. Nijmeijer, J. Physique 48, 185 (1987).

    Article  MathSciNet  Google Scholar 

  9. K.E. Kürten, proceedings of the San Diego Conference (1987).

    Google Scholar 

  10. B. Derrida and G. Weisbuch, J. Physique 47, 1297 (1986).

    Article  Google Scholar 

  11. B. Derrida and Y. Pomeau, Europhys. Lett. 1, 45 (1986).

    Article  ADS  Google Scholar 

  12. B. Derrida and D. Stauffer, Europhys. Lett. 2, 739 (1986).

    Article  ADS  Google Scholar 

  13. H. Flyvbjerg, Lectures given at the Niels Bohr Institute and Nordita (1987), to be published in Physica Scripta.

    Google Scholar 

  14. B. Derrida, J. Phys. A20 (1987) to appear.

    Google Scholar 

  15. B. Derrida, E. Gardner, A. Zippelius, Europhys. Lett. 4, 167 (1987).

    Article  ADS  Google Scholar 

  16. B. Derrida, J.P. Nadal, preprint (1987).

    Google Scholar 

  17. G. Weisbuch, D. Stauffer, J. Physique 48, 11 (1987).

    Article  Google Scholar 

  18. L. de Arcangelis, J. Phys. A20, L369 (1987).

    Google Scholar 

  19. L. de Arcangelis, D. Stauffer, preprint (1987).

    Google Scholar 

  20. B. Derrida, Les Houches (1986) “Chance and Matter”, J. Souletie, J. Vannimenus and R. Stora eds, in press.

    Google Scholar 

  21. M. Mezard, G. Parisi, N. Sourlas, G. Toulouse, M. Virasoro, Phys. Rev. Lett. 52 1146 (1984); J. Physique 45, 843 (1984).

    Article  ADS  Google Scholar 

  22. M. Mezard, G. Parisi, M. Virasoro, J. Physique Lett. 46, 217 (1985).

    Article  Google Scholar 

  23. D. Sherrington, S. Kirkpatrick, Phys. Rev. Lett. 35, 1972 (1975); Phys. Rev. B 17, 4384 (1978).

    Google Scholar 

  24. B. Derrida, Phys. Rev. Lett. 45, 79 (1980); Phys. Rev. B24, 2613 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  25. B. Derrida, G. Toulouse, J. Physique Lett. 46, 223 (1985).

    Article  Google Scholar 

  26. B. Derrida, H. Flyvbjerg, J. Phys. A20 (1987) to appear.

    Google Scholar 

  27. B. Derrida, H. Flyvbjerg, J. Phys. A19, L1003 (1986).

    ADS  Google Scholar 

  28. B. Derrida, H. Flyvbjerg, J. Physique 48, 971 (1987).

    Article  MathSciNet  Google Scholar 

  29. B. Derrida, G. Weisbuch, Europhys. Lett. 4 (1987) to appear.

    Google Scholar 

  30. A. Ogielsky, Phys. Rev. B32, 7384 (1985).

    ADS  Google Scholar 

  31. H. Sompolinsky, Phys. Rev. Lett. 47, 935 (1981).

    Article  ADS  Google Scholar 

  32. H. Sompolinsky, A. Zippelius, Phys. Rev. Lett. 47, 359 (1981); Phys. Rev. B25, 6860 (1982).

    Article  ADS  Google Scholar 

  33. C. de Dominicis, H. Orland, F. Lainée, J. Physique Lett. 46, L463 (1985).

    Article  Google Scholar 

  34. C. de Dominicis, J. of Magnetism and Magnetic Materials 54, 17 (1986).

    Article  ADS  Google Scholar 

  35. K. Binder, A.P. Young, Rev. Mod. Phys. 58, 801 (1986).

    Article  ADS  Google Scholar 

  36. D. Chowdhury, Spin glasses and other frustrated systems (1986), World

    Google Scholar 

  37. Scientific and Co.

    Google Scholar 

  38. D. Stauffer, proceedings of the Antigonish Workshop (1987).

    Google Scholar 

  39. V. Costa, J. Phys. A20, L583 (1987).

    ADS  Google Scholar 

  40. H.E. Stanley, D. Stauffer, J. Kertesz, H.J. Herrmann, preprint (1987).

    Google Scholar 

  41. J.J. Hopfield, Proc. Natl. Aca. Sci. (USA) 79, 2554 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  42. P. Peretto, Biol. Cybern. 50, 51 (1984).

    Article  MATH  Google Scholar 

  43. D.J. Amit, H. Gutfreund, H. Sompolinsky, Ann. of Phys. 173, 30 (1987).

    Article  ADS  Google Scholar 

  44. R. Kree, A. Zippelius, preprint (1987).

    Google Scholar 

  45. E. Gardner, preprints (1987).

    Google Scholar 

  46. J.P. Nadal, G. Toulouse, J.P. Changeux, S. Dehaene, Europhys. Lett. 1, 535 (1986).

    Article  ADS  Google Scholar 

  47. R. Meir, E. Domany, preprints (1987).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Service de Physique Théorique, CEN-Saclay, 91191, Gif-sur-Yvette Cedex, France

    B. Derrida

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  1. B. Derrida
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Editor information

Editors and Affiliations

  1. Accademia dei Lincei, Centro Linceo Interdisciplinare “B. Segre”, Rome, Italy

    Giovanni Gallavotti

  2. Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA

    Paul F. Zweifel

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© 1988 Plenum Press, New York

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Derrida, B. (1988). Dynamics of Automata, Spin Glasses and Neural Network Models. In: Gallavotti, G., Zweifel, P.F. (eds) Nonlinear Evolution and Chaotic Phenomena. NATO ASI Series, vol 176. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1017-4_17

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  • DOI: https://doi.org/10.1007/978-1-4613-1017-4_17

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8294-5

  • Online ISBN: 978-1-4613-1017-4

  • eBook Packages: Springer Book Archive

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