Basic Principles and Concepts in the Physics of Low Dimensional Cooperative Systems

  • Philip Pincus
Part of the Nato Advanced Study Institutes Series book series (NSSB, volume 7)


This NATO institute is devoted to a study of quasi- one and two dimensional systems which exhibit strong electronic correlations. Low dimensionality and strong interactions may lead to many fascinating quasi- ordered states in solids, e.g. magnetism, super conductivity, Peierls distortions, charge or spin density waves, etc. This presentation shall attempt to introduce to students or other non-solid state scientists some of the basic ideas which the author has found to be useful and relevant for thinking and visualizing the systems under investigation. We shall usually not reproduce detailed calculations which we already have available in the literature, but rather attempt to give a feeling for the physical arguments which lead to the predicted results. While our emphasis will lie with theory, the models considered are direct manifestations of the experimentally known nature of the systems under study. We shall present very little detailed experimental results; these have been reviewed by Shchegolev,(1) for the highly conducting ld systems, and by DeJongh and Hiedema(2) and Hone and Richards(3) for the lower dimensionality magnetic systems. Of course, at this institute I expect that much of the most recent work will be presented.


Ising Model Hubbard Model Small Polaron Heisenberg Chain Antibonding State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    I.F. Shchegolev, Phys. Stat. Sol. 12, 9 (1972).Google Scholar
  2. 2.
    L.J. DeJongh and A.R. Midema, Adv. in Physics 23, 1 (1974).Google Scholar
  3. 3.
    D.W. Hone and P.M. Richards, To be Published in Ann. Rev. of Material Science, 4.Google Scholar
  4. 4.
    A good discussion of the Ising model may be found in K. Huang, Statistical Mechanics, (J. Wiley and Sons, New York, 1963 ), Chapters 16, 17.Google Scholar
  5. 5.
    M.E. Fisher, Am. J. Phys. 32, 343 (1964).CrossRefGoogle Scholar
  6. 6.
    M.T. Hutchings, G. Shirane, R.J. Birgeneau, and S.L. Holt, Phys. Rev. B5, 1999 (1972).Google Scholar
  7. 7.
    D.J. Scalapino, M. Sears, and R.A. Ferrell, Phys. Rev. B6, 3409 (1972).CrossRefGoogle Scholar
  8. 8.
    This estimate neglects (a) the fact that the domain must have a closed perimeter, and (b) that some perimeter points have 2 reversed near neighbors. For sufficiently large P these effects are small.Google Scholar
  9. 9.
    L. Onsager, Phys. Rev. 65, 117 (1944).CrossRefGoogle Scholar
  10. 10.
    For a good discussion see Daniel C. Mattis, The Theory of Magnetism, ( Harper and Row, New York, 1965 ) Chapter 8.Google Scholar
  11. 11.
    J.W. Stout and R.C. Chisholm, J.Chem. Phys. 36, 979 (1962) have treated the Ising Model. The method has been elaborated and extended to other magnetic systems as well as coupled superconducting strands by D.Scalapino, Y. Imry, P. Pincus, To Be Published.Google Scholar
  12. 12.
    This is established by nuclear quadrapole resonance experiments in Li+ TCNQ- by J. Murgich and S. Pissanetzky, Chem. Phys. Letters 18, 420 (1973).Google Scholar
  13. 13.
    There also exist stacked structures of the type cation-anioncation-anion; e.g TMPD+ - TCNQ-. We shall not discuss these further here becuase they are intrinsfcally semiconducting not metallic.Google Scholar
  14. 14.
    C.J. Fritchie, Acta Cryst. 20, 892 (1966).CrossRefGoogle Scholar
  15. 15.
    P. Pincus, Solid State Comm. 11, 51 (1972).CrossRefGoogle Scholar
  16. 16.
    P. Chaikin, A.F. Garito, and A.J. Heeger, Phys. Rev. B5, 4966 (1972) P. Chaikin, A.F. Garito, and A.J. Heeger, J. Chem. Phys. 58, 2336 (1973).CrossRefGoogle Scholar
  17. 17.
    See for example C. Kittel, Quantum Theory of Solids, (J. Wiley and Sons, Inc., New York, 1964 ) Chapt. 5.Google Scholar
  18. 18.
    For the case of TTF-TCNQ, t has been calculated by A.J. Berlinsky, J.F. Carolan, and L.Weiler, [Solid State Comm., To be Published], to be about 0.1ev.Google Scholar
  19. 19.
    J. Hubbard, Proc. Roy. Soc. (London) A276, 238 (1963); A237 (1963); A281, 401 (1964).Google Scholar
  20. 20.
    J. Kanamori, Prog. Theo. Physics (Kyoto) 30, 275 (1963).CrossRefGoogle Scholar
  21. 21.
    J.G. Vegter, J. Kommandeur, and P.A. Fedders, Phys. Rev. B7, 2929 (1973); J.G. Vegter and J. Kommandeur, Phys. Rev. B9, 5150 (1974).Google Scholar
  22. 22.
    R.E. Peierls, Quantum Theory of Solids, (Oxford Univ. Press, London, 1955 ), Chapter V.Google Scholar
  23. 23.
    Indeed G. Beni, Solid State Comm., To Be Published, has shown that if d>l, the electron bandwidth arising from transfer between strands tends very strongly to supress the instability.Google Scholar
  24. 24.
    J.G. Vegter, P.I. Kuindersma, and J. Kommadandeur, in N. Klein, D.S. Tannhauser, and M. Pollak, eds. Conduction in Low Mobility Materials, ( Taylor and Francis Ltd., London, 1971 p. 213.Google Scholar
  25. 25.
    L.B. Coleman, M.J. Cohen, D.J. Sandman, F.G. Yamagishi, A.F. Garito, and A.J. Heeger, Solid State Comm. 12, 1125 (1973); D.B. Tanner, C.S. Jacobsen, A.F. Garito, and A.J. Heeger, Phys. Rev. Letters 32, 1301 ( 1974 ); M.J. Cohen, L.B. Coleman, A.F. Garito, and A.J. Heeger, Phys. Rev. B. To Be Published.Google Scholar
  26. 26.
    A.J. Epstein, S. Etemad, A.F. Garito, and A.J. Heeger, Phys. Rev. B5, 952 (1972).CrossRefGoogle Scholar
  27. 27.
    N.F. Mott, Proc. Phys. Soc. (London) A62, 416 (1949).Google Scholar
  28. 28.
    A. Bloch, R.B. Wiseman, and C.M. Varma, Phys. Rev. Letters 28, 753 (1972).CrossRefGoogle Scholar
  29. 29.
    R.E. Borland, Proc. Phys. Soc. London 78, 926 (1901) N.F. Mott and W.D. Twose, Advan. Phys. 10, 107 (1961)Google Scholar
  30. 30.
    N.F. Mott, Phil. Mag. 19, 835 (1969); V. Ambegaokar, B.I. B.I. Halperin, and J.S. Langer, Phys. Rev. B4, 2612 (1971).CrossRefGoogle Scholar
  31. 31.
    E. Ehrenfreund, S. Etemad, L.B. Coleman, E.F. Rybaczewski, A.F. Garito, and A.J. Heeger, Phys. Rev. Letters 29, 269 (1972).CrossRefGoogle Scholar
  32. 32.
    Of course the dimer Hubbard model (C.3) is exactly soluble. See article by P. Pincus in de Laredo and Jurisic, (eds) Selected Topics in Physics, Astrophysics, and Biophysics ( D. Reidel, Dordecht, 1973 ).Google Scholar
  33. 33.
    J. des Cloizeaux and J. Pearson, Phys. Rev. 128, 2131 (1962).CrossRefGoogle Scholar
  34. 34.
    P. Pincus, Solid State Comm. 9, 1971 (1971); G. Beni and P. Pincus, J. Chem. Phys. 57, 3531 (1972); G. Beni, J. Chem. Phys. 58, 3200 (1973).Google Scholar
  35. 35.
    Experimental arguments for U ti t in the alkali salts is given by S. K. Khanna, A.A.Bright, A.F. Garito and A.J. Heeger, Phys. Rev. To Be Published.Google Scholar
  36. 36.
    An excellent general review of the electronic properties and spin dynamics in the TCNQ salts will appear in Z. Soos, Ann. Rev. Phys. Chem. 25, (1974) To Be Published.Google Scholar
  37. 37.
    A. Ovchinnikov, Soviet Physics JETP 30, 1160 (1970) has calculated exactly the low lying excitations in this model of both the conducting and triplet types. Indeed he finds that so long as U>0, the uniform chain is a semiconductor.Google Scholar
  38. 38.
    C.F. Coll III, Phys. Rev. B9, 2150 (1974).CrossRefGoogle Scholar
  39. 39.
    A.A. Ovchinnikov, I.I. Ukrainskii, and G.V. Kventsel, Soviet Physics Uspekhi 15, 575 (1973).CrossRefGoogle Scholar
  40. 40.
    G. Beni and P. Pincus, Phys. Rev. B9, 2963 (1974).CrossRefGoogle Scholar
  41. 41.
    A.A. Bright, A.F. Garito, and A.J. Heeger, Solid State Comm. 13, 943 (1973). A.A.Bright, A.F. Garito, and A.J. Heeger, Phys. Rev. B. To Be Published.Google Scholar
  42. 42.
    P.M. Grant, R.L. Greene, G.C. Wrighton, and G. Castro, Phys. Rev. Letters 31, 1311 (1973).CrossRefGoogle Scholar
  43. 43.
    P. F. Williams and A.N. Bloch, Phys. Rev. B10, 1097 (1974).CrossRefGoogle Scholar
  44. 44.
    H. Gutfreund, B. Horovitz and M. Weger, Solid State Comm. To Be Published.Google Scholar
  45. 45.
    The detailed study of small polaron motion has been carried out by T. Holstein and his coworkers in precisely this model. See for example: T. Holstein, Ann. Phys. 8, 325 (1959); T. Holstein, Ann. Phys. 8, 343 (1959); L. Freedman and T. Holstein, Ann. Phys. 21, 494 (1963); D. Emin and T. Holstein, Ann. Phys. 53, 439 (1969).Google Scholar
  46. 46.
    The details depend somewhat on the nature of the extra degree of freedom to which the electron is coupled. The result given here assumes that this is a simple harmonic oscillator. R. Bari, Phys. Rev. Letters 30, 790 (1973) has considered the opposite limit of a two level system which he feels is more suited for the excitonic polarons.Google Scholar
  47. 47.
    G. Beni, P. Pincus, and J. Kanamori, Phys. Rev. To Be Published.Google Scholar
  48. 48.
    R. Bari, Phys. Rev. B9, 4329 (1974).CrossRefGoogle Scholar
  49. 49.
    C.F. Coll III, and G7Theni, Solid State Comm., To Be Published.Google Scholar
  50. 50.
    As a first step in this direction see A.F. Garito and A.J. Heeger, Accounts of Chem. Res. 7, 232 (1974).Google Scholar

Copyright information

© Springer Science+Business Media New York 1975

Authors and Affiliations

  • Philip Pincus
    • 1
  1. 1.Department of PhysicsUniversity of California Los AngelesUSA

Personalised recommendations