Abstract
Some applications of ultrametric and hierarchical structures are discussed in the context of condensed matter physics. It is shown that a simple arrangement of barriers leads to the Vogel-Fulcher law for the diffusion contant. Evidence is given that in this model the Vogel-Fulcher law is independent of the Kohlrausch-Williams-Watts law for relaxation.
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References
R. Balian, R. Maynard, and G. Toulouse, inLes Mouches Sessions, Ill Condensed Matter (North-Holland, 1978); I. Morgenstern and L. van Hemmen, inHeidelberg Colloquium on Spin Glasses (Springer, Heidelberg, 1983).
J. J. Hopfield,Proc. Natl. Acad. Sci. USA 79:2554 (1982).
M. Mezard and G. Parisi,J. Phys. (Paris) 47:1285 (1986).
H. Orland,J. Phys. Lett. (Paris) 46:L763 (1985).
Y. Fu and P. W. Anderson,J. Phys. A 19:1605 (1986).
N. Rivier and A. L. Lawrence,J. Phys. (Paris) C8-409 (1985).
K. L. Ngai and G. B. Wright (eds.),Relaxation in Complex Systems (U.S. Government Printing Office, 1985).
H. Vogel,Phys. Z. 22:645 (1921); G. S. Fulcher,Am. Ceram. Soc. 6:339 (1925).
P. W. Anderson, inLes Houches Sessions, Ill Condensed Matter (North-Holland, 1978).
K. Binder and A. P. Young,Rev. Mod. Phys. 58:801 (1986).
J. Souletie and J. J. Prejean, inLes Hauches Session “Chance and Matter” (1986).
R. G. Palmer, D. L. Stein, E. Abrahams, and P. W. Anderson,Phys. Rev. Lett. 53:958 (1984).
A. Ogielski and D. L. Stein,Phys. Rev. Lett. 55:1634 (1985).
M. H. Cohen and G. S. Grest,Phys. Rev. B 20:1077 (1979).
S. F. Edwards and T. Vilgis, inPhysics of Disordered Materials D. Adler, H. Fritsche, and S. R. Ovshinski, eds. (Plenum Press, New York, 1985).
S. Teitel and E. Domany,Phys. Rev. Lett. 55:2176 (1985).
T. Vilgis,J. Phys. A: Math. Gen. 20:757 (1987).
M. Mezard, G, Parisi, N. Sourlas, G. Toulouse, and M. Virasoro,Phys. Rev. Lett. 52:1156 (1984).
R. Rammal, G. Toulouse, and M. Virasoro,Rev. Mod. Phys., to appear.
S. Alexander, J. Bernasconi, W. Schneider, and R. Orbach,Rev. Mod. Phys. 53:175 (1981).
G. Paladin, M. Mezard, and C. de Dominics,J. Phys. Lett. (Paris) 46:L985 (1985).
M. Schreckenberg and J. Zittartz, inHeidelberg Colloquium on Glassy Dynamics (1986) to appear.
N. Boccara and M. Daoud (eds.),Physics of Finely Divided Matter (Springer, Heidelberg, 1985).
P. G. de Gennes,Recherche 7:919 (1976).
A. Coniglio, inPhysics of Finely Divided Matter, N. Boccara and M. Daoud, eds. (Springer, Heidelberg, 1985).
S. Alexander and R. Orbach,J. Phys. Lett. (Paris) 43:L625 (1983); R. Rammal and G. Toulouse,J. Phys. Lett. (Paris) 44:L13 (1983).
G. H. Weiss and R. J. Rubin,Adv. Chem. Phys. 52:363 (1983).
P. G. de Gennes,J. Chem. Phys. 76:3316 (1982).
G. Zumofen, A. Blumen, and J. Klafter,J. Chem. Phys., to appear.
R. Zwanzig,J. Stat. Phys. 28:127 (1982).
B. A. Huberman and M. Kerszberg,J. Phys. A 18:L331 (1985).
T. Vilgis, in preparation.
S. F. Edwards and T. Vilgis,Physica Scripta, to appear.
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Vilgis, T.A. On the dynamics of simple hierarchical systems. J Stat Phys 47, 133–148 (1987). https://doi.org/10.1007/BF01009038
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DOI: https://doi.org/10.1007/BF01009038