Abstract
The phenomenon of slow relaxation is discussed with emphasis on finding a general explanation of its ubiquity. After a review of the phenomenon, possible causes are considered both at the microscopic level and from a configuration space viewpoint. Quenched randomness and strongly constrained dynamics appear most important microscopically. In configuration space the central requirement seems to be the existence of many valleys connected sparsely in a hierarchical way. Recent toy models are shown to fit into this overall picture.
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K.S. Cole and R.H. Cole, J. Chem. Phys. 9, 341 (1941).
D.W. Davidson and R.H. Cole, J. Chem. Phys. 19, 1484 (1951).
R. Kohlrausch, Pogg. Ann. Phys. 91, 198 (1854).
G. Williams and D.C. Watts, Trans. Faraday Soc. 66, 80 (1970).
J.L. van Hemmen and A. Sütő, Z. Phys. B 61, 263 (1985).
M. Randeria, J.P. Sethna, and R.G. Palmer, Phys. Rev. Lett. 54, 1321 (1985).
A.T. Ogielski, Phys. Rev. B 32, 7384 (1985).
S. Bernstein, Acta. Math. 52, 1 (1928); see also E. Lieb, Phys. Rev. Lett. 48, 1057 (1982).
H. Vogel, Physik Z. 22, 645 (1921); G.S. Fulcher, J. Am. Ceram. Soc. 77, 3701 (1925); G. Tamman and W. Hesse, Z. Anorg. Allgem. Chem. 156, 245 (1926).
J. Souletie and J.L. Tholence, Phys. Rev. B 32, 516 (1985).
R.G. Palmer, Adv. Phys. 31, 669 (1982); and in Heidelberg Colloquium on Spin Glasses, edited by J.L. van Hemmen and I. Morgenstern (Springer-Verlag, Berlin 1983), p.234.
D.J. Thouless, P.W. Anderson, and R.G. Palmer, Philos. Mag. 35, 593 (1977).
G. Parisi, J. Phys. A 13, L115 (1980).
H. Sompolinsky and A. Zippelius, Phys. Rev. B 25, 6860 (1982).
R.G. Palmer, D.L. Stein, E. Abrahams, and P.W. Anderson, Phys. Rev. Lett. 53, 958 (1984).
R.G. Palmer, to be published in Ann. NY Acad. Sci., 1986.
D.S. Fisher and D.A. Huse, Phys. Rev. Lett. 56, 1601 (1986); and to be published.
R.G. Palmer and D.L. Stein in Relaxations in Complex Systems, edited by K.L. Ngai and G.B. Wright (U.S. Government Printing Office, Washington DC 1985-461-700/20001), 253.
The term rough was apparently first used in this context by J.L. van Hemmen, J. Phys. C 19, L379 (1986).
M. Mézard, G. Parisi, N. Sourlas, G. Toulouse, and M. Virasoro, Phys. Rev. Lett. 52, 1156 (1984); see also R. Rammal, G. Toulouse, and M.A. Virasoro, Rev. Mod. Phys. 58, 765 (1986).
I.A. Campbell, J. Phys. (Paris) Lett. 46, L1159 (1985); Phys. Rev. B 33, 3587 (1986).
S. Alexander and R. Orbach, J. Phys. (Paris) Lett. 43, L625 1982.
E.g., J.H. Gibbs and E.A. Dimarzio, J. Chem. Phys.28, 373 (1958); E.A. Dimarzio and J.H. Gibbs, J. Chem. Phys.28, 807 (1958).
R.V. Chamberlin, G. Mozurkewich, and R. Orbach, Phys. Rev. Lett. 52, 867 (1984). However β→ 1/3 is not evident in later results by the same group, and other groups dispute the interpretation of the data in terms of a stretched exponential fit. See R. Hooger beets, W.L. Luo, and R. Orbach, Phys. Rev. B 34, 1719 (1986); J.L. van Hemmen and G.J. Nieuwenhuys, Europhys. Lett. 2, 797 (1986); P. Nordblad, L. Lundgren, P. Svedlindh, L. Sandlund, and P. Granberg, Phys. Rev. B _, (1987).
B.A. Huberman and M. Kerszberg, J. Phys. A 18, L331 (1985).
A.T. Ogielski and D.L. Stein, Phys. Rev. Lett. 55, 1634 (1985).
S. Grossman, F. Wegner, and K.H. Hoffmann, J. Phys. (Paris) Lett. 46, L575 (1985).
S. Teitel and E. Domany, Phys. Rev. Lett. 55, 2176 (1985); 56, 1755 (1986).
M. Schreckenberg, Z. Phys. B 60, 483 (1985).
G. Paladin, M. Mézard, and C. De Dominicis, J. Phys. (Paris) Lett. 46, L985 (1985).
P. Sibani, NORDITA preprint, 1985.
D. Kumar and S.R. Shenoy, Solid State Commun. 57, 927 (1986).
A. Blumen, J. Klafter, and G. Zumofen, J. Phys. A 19, L77 (1986).
A. Maritan and A.L. Stella, J. Phys. A 19, L269 (1986); Phys. Rev. Lett. 56, 1754 (1986); Phys. Rev. B 34, 456 (1986).
C.P. Bachas and B.A. Huberman, Phys. Rev. Lett. 57, 1965 (1986).
C. De Dominicis, H. Orland, and F. Lainée, J. Phys. (Paris) Lett. 46, L463 (1985).
G.H. Fredrickson and H.C. Andersen, Phys. Rev. Lett. 53, 1244 (1984); J. Chem. Phys. 83, 5822 (1985).
G.H. Fredrickson and S.A. Brawer, J. Chem. Phys. 84, 3351 (1986).
G. Adam and J.H. Gibbs, J. Chem. Phys. 43, 139 (1965).
J.L. Skinner, J. Chem. Phys. 79, 1955 (1983); J. Budimir and J.L. Skinner, J. Chem. Phys. 82, 5232 (1985).
J.C. Kimball, J. Stat. Phys. 21, 289 (1979).
F.H. Stillinger and T.A. Weber, to be published in Ann. NY Acad. Sci., 1986; T.A. Weber, G.H. Fredrickson, and F.H. Stillinger, Phys. Rev. B 34, (1986); T.A. Weber and F.H. Stillinger, Phys. Rev. B _, (1987).
S.H. Glarum, J. Chem. Phys. 33, 1371 (1960); P. Bordewijk, Chem. Phys. Lett. 32, 592 (1975).
J. Klafter and A. Blumen, Chem. Phys. Lett. 119, 377 (1985); G. Zumofen, A. Blumen, and J. Klafter, J. Chem. Phys. 82, 3198 (1985).
M.F. Shlesinger and E.W. Montroll, Proc. Nat]. Acad. Sci. USA 81, 1280 (1984); M.F. Shlesinger, J. Stat. Phys. 36, 639 (1984).
S. Redner and K. Kang, J. Phys. A 17, L451 (1984).
J.T. Bendler, J. Stat. Phys. 36, 625 (1984); J.T. Bendler and M.F. Shlesinger, Macromolecules 18, 591 (1985).
T. Förster, Z. Naturforsch. Teil A 4, 321 (1949).
A. Blumen, Nuovo Cimento B 63, 50 (1981).
J. Klafter and M.F. Shlesinger, Proc. Natl. Acad. Sci. USA 83, 848 (1986).
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Palmer, R.G. (1987). Relaxation in complex systems. In: van Hemmen, J.L., Morgenstern, I. (eds) Heidelberg Colloquium on Glassy Dynamics. Lecture Notes in Physics, vol 275. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0057523
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DOI: https://doi.org/10.1007/BFb0057523
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