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Application of the Real-Space Renormalization to Adsorbed Systems

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Book cover Real-Space Renormalization

Part of the book series: Topics in Current Physics ((TCPHY,volume 30))

Abstract

The application of real-space renormalization-group methods to the description of order-disorder transitions that occur in adsorbed systems is described. Preservation of symmetries of the ground states by the renormalization-group transformation is stressed. Two methods that ensure this are presented: the sublattice method and the prefacing transformation. The concept of the vacancy, often associated with the use of the latter method, is introduced and the simplicity that it brings to the description of first-order transitions is emphasized. As an example, the description of the ferromagnetic transition of the two-dimensional q-state Potts model is reviewed. Numerous applications of these methods to problems in statistical physics are noted.

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References

  1. J. Phys. (Paris) 38, C-4 (1973)

    Google Scholar 

  2. M. Bretz, J.G. Dash, D.C. Hickernell, E.O. McLean, O.E. Vilches: Phys. Rev. A8, 1589 (1973)

    Google Scholar 

  3. M. Bretz, J.G. Dash, D.C. Hickernell, E.O. McLean, O.E. Vilches: Erratum, Phys. Rev. A9, 2814 (1974)

    ADS  Google Scholar 

  4. D.M. Butler, J.A. Litzinger, G.A. Stewart, R.B. Griffiths: Phys. Rev. Lett. 42, 1289 (1979)

    Google Scholar 

  5. D.M. Butler, J.A. Litzinger, G.A. Stewart: Phys. Rev. Lett. 44, 466 (1980)

    Article  ADS  Google Scholar 

  6. A. Thorny, X. Duval: J. Chem. Phys. 66, 1966 (1969); 67, 286 (1970); 67, 1101 (1970)

    Google Scholar 

  7. G.A. Somorjai, M.A. Van Hove: Adsorbed Monolayers on Solid Surfaces, Struc- ture and Bonding, Vol. 38 ( Springer, Berlin, Heidelberg, New York 1979 )

    Google Scholar 

  8. M.E. Fisher: Rep. Prog. Phys. 30, 615 (1967)

    Google Scholar 

  9. E.M. Lifshitz, L.P. Pitaevskii: Statistical Physics, 3rd ed. (Pergamon, Oxford 1980) Pt.1, Chap.14

    Google Scholar 

  10. J.M.J. van Leeuwen: Phys. Rev. Lett. 34, 1056 (1975)

    Article  ADS  Google Scholar 

  11. B. Nienhuis, M. Nauenberg: Phys. Rev. B13, 2021 (1976)

    ADS  Google Scholar 

  12. M. Schick, J.S. Walker, M. Wortis: Phys. Rev. B16, 2205 (1977)

    ADS  Google Scholar 

  13. A.N. Berker, S. Ostlund, F.A. Putnam: Phys. Rev. B16, 2205 (1977)

    Google Scholar 

  14. S. Ostlund, A.N. Berker: Phys. Rev. Lett. 42, 843 (1979)

    Article  ADS  Google Scholar 

  15. P.M. Horn, R.J. Birgeneau, P. Heiney, E.M. Hammonds: Phys. Rev. Lett. 41, 961 (1978)

    Article  ADS  Google Scholar 

  16. R.B. Potts: Proc. Cambridge Philos. Soc. 48, 106 (1952)

    MathSciNet  MATH  Google Scholar 

  17. F.Y. Wu: Rev. Mod. Phys. (to be published)

    Google Scholar 

  18. S. Alexander: Phys. Lett. A54, 353 (1975)

    ADS  Google Scholar 

  19. E. Domany, M. Schick, J.S. Walker: Phys. Rev. Lett. 38, 1148 (1977)

    Article  ADS  Google Scholar 

  20. E. Domany, M. Schick, J.S. Walker, R.B. Griffiths: Phys. Rev. B18, 2209 (1978)

    ADS  Google Scholar 

  21. R.J. Baxter: J. Phys. C6, L445 (1973)

    ADS  Google Scholar 

  22. B. Nienhuis, A.N. Berker, E.K. Riedel, M. Schick: Phys. Rev. Lett. 43, 737 (1979)

    Article  ADS  Google Scholar 

  23. M. Bretz, J.G. Dash: Phys. Rev. Lett. 27, 647 (1971)

    Article  ADS  Google Scholar 

  24. R.L. Elgin, D.L. Goodstein: Phys. Rev. A9, 2657 (1974)

    Google Scholar 

  25. S.V. Hering, S.W. Van Sciver, O.E. Vilches: J. Low Temp. Phys. 25, 793 (1976)

    Article  ADS  Google Scholar 

  26. M. Bretz: Phys. Rev. Lett. 38, 501 (1977)

    Article  ADS  Google Scholar 

  27. M. Nielson, J.P. McTague, W. Ellenson: J. Phys. (Paris) 38, C4–10 (1977)

    Google Scholar 

  28. Th. Niemeijer, J.M.J. van Leeuwen: Phys. Rev. Lett. 31, 1411 (1973); Physica (Utrecht) 71, 17 (1974)

    Article  ADS  Google Scholar 

  29. M.P.N. den Nijs, A.M.M. Pruisken, J.M. J. van Leeuwen: Physica (Utrecht) A84, 539 (1976)

    Google Scholar 

  30. R.J. Baxter, F.Y. Wu: Phys. Rev. Lett. 31, 1924 (1973); Aust. J. Phys. 27, 357 (1954)

    MathSciNet  Google Scholar 

  31. R.M.F. Houtappel: Physica (Utrecht) 16, 425 (1950)

    Google Scholar 

  32. G. Wannier: Phys. Rev. 79, 357 (1950). Note that the numerical value of the entropy quoted by Wannier is incorrect. The correct value is given in our text

    Google Scholar 

  33. J. Stephenson: J. Math. Phys. 5, 1009 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  34. S. Alexander, P. Pincus: J. Phys. A13, 263 (1980)

    ADS  Google Scholar 

  35. R.J. Baxter: J. Phys. A23, L61 (1980)

    MathSciNet  Google Scholar 

  36. W. Kinzel, M. Schick: Phys. Rev. B23, 3435 (1981)

    ADS  Google Scholar 

  37. K. Subbaswamy, G.D. Mahan: Phys. Rev. Lett. 37, 642 (1976)

    Article  ADS  Google Scholar 

  38. G.D. Mahan, F.H. Claro: Phys. Rev. B16, 1168 (1977)

    ADS  Google Scholar 

  39. B. Nienhuis, Aa.S. Sudbd, E.H. Hauge: Physica 92A, 222 (1978)

    Google Scholar 

  40. G.D. Mahan, S.M. Girvin: Phys. Rev. B17, 4411 (1978)

    ADS  Google Scholar 

  41. M. Schick, R.B. Griffiths: J. Phys. A10, 2123 (1977)

    ADS  Google Scholar 

  42. A.P. Young, D.A. Lavis: J. Phys. Al2, 229 (1979)

    Google Scholar 

  43. A.J. Berlinsky, W.G. Unruh, W.R. McKinnion, R.R. Haering: Solid State Commun. 31, 135 (1979)

    Google Scholar 

  44. W. Kinzel, M. Schick, A.N. Berker: In Ordering in Two Dimensions, ed. by S. Sinha (Elsevier, Amsterdam 1980 ) p. 381

    Google Scholar 

  45. M. Bretz: Ph. D. Thesis, Univ. of Washington (1971)

    Google Scholar 

  46. J.K. Kjems, L. Passell, H. Taub, J.G. Dash: Phys. Rev. Lett. 32, 724 (1974)

    Google Scholar 

  47. J.K. Kjems, L. Passell, H. Taub, J.G. Dash, A.D. Novaco: Phys. Rev. B13, 1446 (1976)

    ADS  Google Scholar 

  48. J. Suzanne, J.P. Coulomb, M. Bienfait: Surf. Sci. 40, 414 (1973)

    Article  ADS  Google Scholar 

  49. T.T. Chung, J.G. Dash: Surf. Sci. 66, 559 (1977)

    Article  ADS  Google Scholar 

  50. Y. Larher: J. Chem. Soc. Faraday Trans. I70, 320 (1974)

    Google Scholar 

  51. F.A. Putnam, T. Fort, Jr.: J. Phys. Chem. 79, 459 (1975), and 81, 2164 (1977)

    Google Scholar 

  52. F.A. Putnam, T. Fort, Jr., R.B. Griffiths: J. Phys. Chem. 81, 2171 (1977)

    Article  Google Scholar 

  53. D.M. Butler, G.B. Huff, R.W. Togh, G.A. Stewart: Phys. Rev. Lett. 35, 1718 (1975)

    Article  ADS  Google Scholar 

  54. W.F. Brooks: Ph. D. Thesis, Stevens Institute of Technology (1977)

    Google Scholar 

  55. J.S. Walker, M. Schick: Phys. Rev. B20, 2088 (1979)

    ADS  Google Scholar 

  56. S. Ostlund, A.N. Berker: Phys. Rev. B21, 5410 (1980)

    ADS  Google Scholar 

  57. T.W. Burkhardt, W. Kinzel: Phys. Rev. B20, 4730 (1979)

    ADS  Google Scholar 

  58. C. Dasgupta: Phys. Rev. B15, 3460 (1977)

    Google Scholar 

  59. M.P.M. den Nijs: Physica (Utrecht) A95, 449 (1979), and references therein

    Google Scholar 

  60. B. Nienhuis, M. Nauenberg: Phys. Rev. Lett. 35, 477 (1975)

    Article  ADS  Google Scholar 

  61. J.M. Kosterlitz: J. Phys. C 7, 1046 (1974)

    Article  ADS  Google Scholar 

  62. M.P.M. den Nijs: J. Phys. Al2, 1857 (1979)

    Google Scholar 

  63. B. Nienhuis, E.K. Riedel, M. Schick: J. Phys. A13, L31 (1980)

    MathSciNet  ADS  Google Scholar 

  64. B. Nienhuis, E.K. Riedel, M. Schick: J. Phys. A13, L189 (1980)

    MathSciNet  ADS  Google Scholar 

  65. T.W. Burkhardt: Z. Phys. B39, 159 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  66. J.L. Black, V.J. Emery: Phys. Rev. B23, 429 (1981)

    ADS  Google Scholar 

  67. R.B. Pearson: Phys. Rev. B22, 2579 (1980)

    ADS  Google Scholar 

  68. H.W.J. Blöte, M.P. Nightingale, B. Derrida: J. Phys. A14, L45 (1981)

    ADS  Google Scholar 

  69. R.J. Birgeneau, G.S. Brown, P.M. Horn, D.E. Moncton, P.W. Stephens: J. Phys. C14, L49 (1981)

    ADS  Google Scholar 

  70. M. Nauenberg, D.J. Scalapino: Phys. Rev. Lett. 44, 837 (1980)

    Google Scholar 

  71. J.L. Cardy, M. Nauenberg, D.J. Scalapino: Phys. Rev. B22, 2560 (1980)

    Google Scholar 

  72. L.P. Kadanoff: Phys. Rev. B22, 2560 (1980)

    Google Scholar 

  73. M. Blume, V.J. Emery, R.B. Griffiths: Phys. Rev. A4, 1071 (1971)

    ADS  Google Scholar 

  74. M.J. Tejwani, 0. Ferreira, 0.E. Vilches: Phys. Rev. Lett. 44, 152 (1980)

    Article  ADS  Google Scholar 

  75. A.N. Berker, D.R. Nelson: Phys. Rev. B19, 2488 (1979)

    ADS  Google Scholar 

  76. E.K. Riedel: Physica 106A, 110 (1981)

    Google Scholar 

  77. B. Nienhuis, E.K. Riedel, M. Schick: To be published

    Google Scholar 

  78. B. Nienhuis, E.K. Riedel, M. Schick: Phys. Rev. B23, 6055 (1981)

    ADS  Google Scholar 

  79. A.N. Berker, D. Andleman, A. Aharony: J. Phys. A13, L413 (1980)

    Google Scholar 

  80. D. Andelman, A.N. Berker: J. Phys. A14, L91 (1981)

    ADS  Google Scholar 

  81. V. Mizrahi, E. Domany: Phys. Rev. B24, 4008 (1981)

    ADS  Google Scholar 

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Authors
  1. M. Schick
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Editors and Affiliations

  1. Institut Laue-Langevin, 156 X, F-38042, Grenoble Cédex, France

    Theodore W. Burkhardt

  2. Department of Physics, Temple University, 19122, Philadelphia, PA, USA

    Theodore W. Burkhardt

  3. Laboratorium voor Technische Natuurkunde, Technische Hogeschool Delft, Lorentzweg 1, 2600 GA, Delft, The Netherlands

    J. M. J. van Leeuwen

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© 1982 Springer-Verlag Berlin Heidelberg

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Schick, M. (1982). Application of the Real-Space Renormalization to Adsorbed Systems. In: Burkhardt, T.W., van Leeuwen, J.M.J. (eds) Real-Space Renormalization. Topics in Current Physics, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81825-7_6

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  • DOI: https://doi.org/10.1007/978-3-642-81825-7_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-81827-1

  • Online ISBN: 978-3-642-81825-7

  • eBook Packages: Springer Book Archive

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