Advertisement

Random walks with memory

  • L. Peliti
  • L. Pietronero
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    L. Pietronero andE. Tosatti:Fractals in Physios (North-Holland, Amsterdam, New York, N. Y., 1986).Google Scholar
  2. [2]
    P. G. de Gennes:Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, N. Y., 1979).Google Scholar
  3. [3]
    P. J. Flory:Principles of Polymer Chemistry (Cornell University Press, Ithaca, N. Y., 1953).Google Scholar
  4. [4]
    L. Pietronero:Phys. Rev. B,27, 5887 (1983).ADSCrossRefGoogle Scholar
  5. [5]
    D. J. Amit:Field Theory, the Renormalization Group and Critical Phenomena (McGraw-Hill Int., New York, N. Y., 1978).Google Scholar
  6. [6]
    F. Spitzer:Principles of Random Walk (Springer-Verlag, New York, N. Y., 1976).CrossRefMATHGoogle Scholar
  7. [7]
    G. H. Weiss andE. J. Rubin:Adv. Chem. Phys.,62, 363 (1983). For the random walk in disordered media that we do not discuss here seeS. Alexander, J. Bernasconi, W. R. Schneider and R. Orback:Rev. Mod. Phys.,53, 175 (1981);M. F. Shlesinger and E. W. Montroll:Proc. Natl. Acad. Sci. USA,81, 1280 (1984).Google Scholar
  8. [8]
    B. B. Mandelbrot:The Fractal Geometry of Nature (W. H. Freeman, New York, N. Y., 1983).Google Scholar
  9. [9]
    W. R. Schneider: inTrends and Developments in the 80’s, Bielefeld Math-Phys. 4 and 5, edited byS. Albeverio andP. Blancherd (World Scientific Publ. Co., Singapore, 1985), p. 349.Google Scholar
  10. [10]
    W. Feller:An Introduction to Probability Theory and its Applications, Vol. 1 and 2 (Wiley, New York, N. Y., 1971).MATHGoogle Scholar
  11. [11]
    M. L. Huggins:J. Phys. Chem.,46, 151 (1942). See also the discussion in Chapt. III of ref. [2].CrossRefGoogle Scholar
  12. [12]
    I. Majid, Z. V. Djordjevic andH. E. Stanley:Phys. Rev. Lett.,51, 1282 (1983).MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    B. Nienhuis:Phys. Rev. Lett.,49, 1062 (1982).MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    S. P. Obukhov:J. Phys. A,17, L965 (1984).ADSCrossRefGoogle Scholar
  15. [15]
    R. Vilanove andF. Rondelez:Phys. Rev. Lett.,45, 1502 (1980);A. Takahashi, A. Yoshida and M. Kawaguchi:Macromolecules,15, 1196 (1982);A. Baumgabtneb:J. Phys. (Paris),43, 1407 (1982);A. L. Kholodenko and K. F. Freed:J. Phys. A,17, L191 (1984);M. J. Stephen:Phys. Lett. A,53, 363 (1975).ADSCrossRefGoogle Scholar
  16. [16]
    P. G. de Gennes:Phys. Lett. A,38, 339 (1972).ADSCrossRefGoogle Scholar
  17. [17]
    L. Peliti: inFractals in Physics (North-Holland, Amsterdam, New York, N. Y., 1986), p. 73;L. Pietronero and L. Peliti: inFractals in Physics (North-Holland, Amsterdam, New York, N. Y., 1986), p. 83.Google Scholar
  18. [18]
    L. Pietronero:Phys. Rev. Lett.,55, 2025 (1985).ADSCrossRefGoogle Scholar
  19. [19]
    L. Pietronero andL. Peliti:Phys. Rev. Lett.,55, 1479 (1985).ADSCrossRefGoogle Scholar
  20. [20]
    L. Peliti:J. Phys. (Paris) Lett.,45, L925 (1984).CrossRefGoogle Scholar
  21. [21]
    P.C. Martin, E. D. Siggia andH.A. Rose:Phys. Rev. A,7, 423 (1973).ADSCrossRefGoogle Scholar
  22. [22]
    L. Peliti:J. Phys. (Paris),46, 1469 (1985).CrossRefGoogle Scholar
  23. [23]
    M. Doi:J. Phys. A,9, 1465, 1479 (1976).ADSCrossRefGoogle Scholar
  24. [24]
    P. Gbassbebger andM. Scheunert:Fortschr. Phys.,28, 547 (1980).MathSciNetCrossRefGoogle Scholar
  25. [25]
    D. J. Amit, G. Parisi andL. Peliti:Phys. Rev. B,27, 1635 (1983).MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    F. J. Wegner:Phys. Rev. B,5, 4529 (1972);6, 1891 (1972).ADSCrossRefGoogle Scholar
  27. [27]
    J. Beenasconi andL. Pietronero:Phys. Rev. B,29, 5196 (1984);S. L. A. de QueiRoz, A. L. Stella and R. B. Stinchcombe:J. Phys. A,17, L45 (1984), and to be published;H. C. Ottinger:J. Phys. A,18, 363 (1985).ADSCrossRefGoogle Scholar
  28. [28]
    E. Kammal, J. C. Anglès D’Auriac andA. Benoit:J. Phys. A,17, L9 (1984).CrossRefGoogle Scholar
  29. [29]
    S. P. Obukhov:J. Phys. A,17, L7 (1984).ADSCrossRefGoogle Scholar
  30. [30]
    S. P. Obukhov andL. Peliti:J. Phys. A,16, L147 (1983).MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    L. Peliti:Phys. Rep.,103, 225 (1984).MathSciNetADSCrossRefGoogle Scholar
  32. [32]
    G. E. Uhlenbeck andL. S. Ornstein:Phys. Rev.,36, 823 (1930).ADSCrossRefMATHGoogle Scholar
  33. [33]
    C. Byrnes andA. J. Guttmann:J. Phys. A,17, 3335 (1984).MathSciNetADSCrossRefGoogle Scholar
  34. [34]
    E. C. Dekeyser: unpublished.Google Scholar
  35. [35]
    J. Adler: private communication.Google Scholar
  36. [36]
    J. W. Lyklema andK. Kremer:J. Phys. A,17, L691 (1984).ADSCrossRefGoogle Scholar
  37. [37]
    I. Majid, N. Jan, A. Coniglio andH. E. Stanley:Phys. Rev. Lett.,52, 1257 (1984).ADSCrossRefGoogle Scholar
  38. [38]
    L. Peliti:J. Phys. (Paris) Lett.,45, L925 (1984).CrossRefGoogle Scholar
  39. [39]
    K. Kremer andJ. W. Lyklema:Phys. Rev. Lett.,55, 2091(C) (1985);J. W. Lyklema and K. Kremer:J. Phys. A,19, 275 (1986).ADSCrossRefGoogle Scholar
  40. [40]
    I. Majid, N. Jan, A. Coniglio and H. E. Stanley: preprint.Google Scholar
  41. [41]
    A. Coniglio and N. Jan: private communication.Google Scholar
  42. [42]
    K. Kremer andJ. W. Lyklema:Phys. Rev. Lett.,54, 267 (1985).ADSCrossRefGoogle Scholar
  43. [43]
    A. Weinrib andS.A. Trugman:Phys. Rev. B,31, 2993 (1985).ADSCrossRefGoogle Scholar
  44. [44]
    J. W. Lyklema:J. Phys. A,18, L617 (1985).ADSCrossRefGoogle Scholar
  45. [45]
    K. Ziff:Phys. Rev. Lett.,56, 545 (1986).ADSCrossRefGoogle Scholar
  46. [46]
    J. W. Lyklema, C. Evertsz andL. Pietronero:Europhys. Lett.,2, 77 (1986);J. W. Lyklema and C. Evertsz: inFractals in Physics (North-Holland, Amsterdam, New York, N. Y., 1986), p. 87.ADSCrossRefGoogle Scholar
  47. [47]
    L. Niemeyer, L. PIetronero andH. J. Wiesmann:Phys. Rev. Lett.,52, 1033 (1984);L. Pietronero and H. J. Wiesmann:J. Stat. Phys.,36, 881 (1984).MathSciNetADSCrossRefGoogle Scholar
  48. [48]
    J. W. Lyklema and C. Evertsz: to be published.Google Scholar
  49. [49]
    T. A. Witten andL. M. Sander:Phys. Rev. Lett.,47, 1400 (1981).ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica 1987

Authors and Affiliations

  • L. Peliti
    • 1
  • L. Pietronero
    • 1
  1. 1.Solid State Physics LaboratoryUniversity of Groningen Melkweg 1GroningenThe Netherlands

Personalised recommendations