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Simulation of Small Systems

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Part of the book series: Topics in Current Physics ((TCPHY,volume 7))

Abstract

Two aspects of small systems are considered. The first is the simulation of systems of small extent and given shape, where surface properties can no longer be neglected in comparison with bulk properties. The second aspect is the appearance of small subsystems as parts of the model system being considered. These latter “clusters” play an essential role for the dynamics of phase transitions. Various aspects such as finite-size scaling behavior, relation between surface and bulk properties and interactions between clusters are discussed. Effective methods for the evaluation of clusters statistics are described in an appendix.

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References

  1. J.K. Lee, J.A. Barker, F.F. Abraham: J. Chem. Phys. 58, 3166 (1973)

    Article  ADS  Google Scholar 

  2. F.F. Abraham: J. Chem. Phys. 61, 1221 (1974)

    Article  ADS  Google Scholar 

  3. J. Miyazaki, G.M. Pound, F.F. Abraham, J.A. Barker: J. Chem. Phys. 67, 3851 (1977) K. Nishioka: Phys. Rev. A 16, 2143 (1977)

    Article  ADS  Google Scholar 

  4. K. Binder, D. Stauffer: J. Stat. Phys. 6, 49 (1972)

    Article  ADS  Google Scholar 

  5. K. Binder: J. Chem. Phys. 63, 2265 (1975)

    Article  ADS  Google Scholar 

  6. J.J. Burton, C.L. Briant: “Atomistic Models of Microclusters”, in Nucleation Phenomena, ed. by A.C. Zettlemoyer (Elsevier, Amsterdam 1977) p. 131

    Google Scholar 

  7. M.R. Hoare, P. Pal: Nature (Phys. Sci.) 236, 35 (1972); J. Crystal Growth 17, 77 (1972)

    ADS  Google Scholar 

  8. J.J. Burton: In Modern Theoretical Chemistry, Vol. 6, ed. by B. Berne (Plenum Press, New York 1977)

    Google Scholar 

  9. J.G. Curro: J. Chem. Phys. 61, 1203 (1974) D.C. Rapaport: J. Phys. A 9, 1521 (1977)

    Article  ADS  Google Scholar 

  10. K. Binder: Phys. Stat. Sol. 46, 567 (1971)

    Article  ADS  Google Scholar 

  11. K. Binder: Physica 62, 508 (1972)

    Article  ADS  Google Scholar 

  12. D.P. Landau: Phys. Lett. A 47, 41 (1973)

    ADS  Google Scholar 

  13. D.P. Landau: Phys. Rev. B 13, 2997 (1976)

    ADS  Google Scholar 

  14. D.P. Landau: Phys. Rev. B 14, 255 (1976)

    ADS  Google Scholar 

  15. T.L. Hill: J. Chem. Phys. 36, 3182 (1962)

    Article  ADS  Google Scholar 

  16. T.L. Hill: Thermodynamics of Small Systems (Benjamin, New York 1963)

    MATH  Google Scholar 

  17. M.E. Fisher, A.E. Ferdinand: Phys. Rev. Lett. 19, 169 (1967)

    Article  ADS  Google Scholar 

  18. A.E. Ferdinand, M.E. Fisher: Phys. Rev. 185, 832 (1969)

    Article  ADS  Google Scholar 

  19. K. Binder, P.C. Hohenberg: Phys. Rev. B 9, 2194 (1974)

    ADS  Google Scholar 

  20. Th.T.A. Paauw, A. Compagner, D. Bedeaux: Physica 79, 1 (1975)

    Article  Google Scholar 

  21. E. Domany, K.K. Mon, G.V. Chester, M.E. Fisher: Phys. Rev. B 12, 5025 (1975)

    ADS  Google Scholar 

  22. E. Kneller: “Theorie der Magnetisierungskurve kleiner Kristalle”, in Ferromagnetismus, Hrsg. H.P.J. Wijn, Handbuch der Physik, Bd. XVIII/2 (Springer, Berlin, Heidelberg, New York 1966), S. 438 I.S. Jacobs, C.P. Bean: In Magnetism, ed. by G.T. Rado, H. Suhl (Academic Press, New York 1963)

    Google Scholar 

  23. K. Binder, H. Rauch, V. Wildpaner: J. Phys. Chem. Sol. 31, 391 (1970)

    Article  ADS  Google Scholar 

  24. K. Binder: Z. Angew. Phys. 30, 51 (1970)

    Google Scholar 

  25. V. Wildpaner: Z. Phys. 270, 215 (1974)

    Article  ADS  Google Scholar 

  26. H. Müller-Krumbhaar, K. Binder: Z. Phys. 254, 269 (1972)

    Article  ADS  Google Scholar 

  27. K. Binder, H. Müller-Krumbhaar: Phys. Rev. B 7, 3297 (1973)

    ADS  Google Scholar 

  28. H.C. Bolton, C.H. Johnson: Phys. Rev. B 13, 3025 (1976)

    ADS  Google Scholar 

  29. J. Feder, K. Rüssel, J. Lothe, M. Pound: Advan. Phys. 15, 117 (1966)

    Article  ADS  Google Scholar 

  30. A. Zettlemoyer (ed.): Nucleation (Dekker, New York 1969); Nucleation II (Marcell Dekker, New York 1977)

    Google Scholar 

  31. K. Binder, D. Stauffer, H. Müller-Krumbhaar: a) Phys. Rev. B 12, 5261 (1975) b) Phys. Rev. B 10, 3853 (1974)

    ADS  Google Scholar 

  32. K. Binder: Phys. Rev. B 15, 4425 (1977)

    ADS  Google Scholar 

  33. J. Hoshen, R. Kopelman: Phys. Rev. B 14, 3438 (1976)

    ADS  Google Scholar 

  34. C. Domb, E. Stoll: J. Phys. A 10, 1141 (1977)

    ADS  Google Scholar 

  35. R. Becker, W. Döring: Ann. Phys. 24, 719 (1935)

    Article  MATH  Google Scholar 

  36. C. van Leeuwen, J.P. van der Eerden: Surface Sci. 64, 237 (1977)

    Article  ADS  Google Scholar 

  37. H. Müller-Krumbhaar, E.P. Stoll: J. Chem. Phys. 65, 4294 (1976)

    Article  ADS  Google Scholar 

  38. H. Müller-Krumbhaar: Phys. Lett. A 48, 459 (1974)

    ADS  Google Scholar 

  39. H. Müller-Krumbhaar: Phys. Lett. A 50, 27 (1974)

    ADS  Google Scholar 

  40. E. Stoll, K. Binder, T. Schneider: Phys. Rev. B 6, 2777 (1972)

    ADS  Google Scholar 

  41. H.E. Stanley: Introduction to Phase Transitions and Critical Phenomena (Clarendon Press, Oxford 1971)

    Google Scholar 

  42. K. Binder: Ann. Phys. (N.Y.) 98, 390 (1976)

    Article  ADS  Google Scholar 

  43. M.E. Fisher: Physics 3, 255 (1967)

    Google Scholar 

  44. C. Domb, T. Schneider, E. Stoll: J. Phys. A 8, L90 (1975)

    ADS  Google Scholar 

  45. H.N.V. Temperley: J. Phys. A 9, L113 (1976)

    ADS  Google Scholar 

  46. H.N.V. Temperley, E.H. Lieb: Proc. R. Soc. A 322, 251 (1971)

    ADS  MathSciNet  Google Scholar 

  47. R.J. Baxter: J. Phys. C 6, L445 (1973)

    ADS  Google Scholar 

  48. J.W. Essam: Discrete Math. 1, 83 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  49. S. Kirkpatrick: Rev. Mod. Phys. 45, 574 (1973) V.K.S. Shante, S. Kirkpatrick: Advan. Phys. 20, 325 (1971)

    Article  ADS  Google Scholar 

  50. J.W. Essam: In Phase Transitions and Critical Phenomena, ed. by C. Domb, M.S. Green, Vol. 2 (Academic Press, New York 1972) p. 197

    Google Scholar 

  51. M.F. Sykes, D.S. Gaunt, J.W. Essam: J. Phys. A 9, L43 (1976) and references

    ADS  Google Scholar 

  52. P. Dean, N.F. Bird: National Laboratory, Teddinqton, England, Rpt. No. MA61 (1966)

    Google Scholar 

  53. D. Stauffer: Phys. Rev. Lett. 35, 394 (1975)

    Article  ADS  Google Scholar 

  54. M.M. Bakri, D. Stauffer: Phys. Rev. B 14, 4215 (1976)

    ADS  Google Scholar 

  55. A. Sur, J.L. Lebowitz, J. Marro, M.H. Kalos, S. Kirkpatrick: J. Statist. Phys. 15, 345 (1976)

    Article  ADS  Google Scholar 

  56. J. Hoshen, D. Stauffer, G.H. Bishop, R.J. Harrison, G.D. Quinn: Preprint, submitted to J. Phys. A 12, 1285 (1979)

    ADS  Google Scholar 

  57. K.J. Duff, V. Canella: AIP Conf. Proc. 10, 541 (1972)

    ADS  Google Scholar 

  58. M.E. Levinshtein, B.I. Shklovskii, M.S. Shur, A.L. Efros: Zh. Eksp. Theor. Fiz. 69, 386 (1975)

    Google Scholar 

  59. G.D. Quinn, G.H. Bishop, R.J. Harrison: J. Phys. A 9, L9 (1976)

    ADS  Google Scholar 

  60. P.L. Leath: Phys. Rev. Lett. 36, 921 (1976); Phys. Rev. B 14, 5046 (1976)

    Article  ADS  Google Scholar 

  61. I. Webman, J. Jortner, M. Cohen: Phys. Rev. B 13, 713 (1976) and references

    ADS  Google Scholar 

  62. T. Odagaki, N. Ogita, H. Matsuda: J. Phys. Soc. Japan 39, 618 (1975)

    Article  ADS  Google Scholar 

  63. A. Coniglio, C.R. Nappi, F. Peruggi, L. Russo: J. Phys. A 10, 205 (1977) and references

    ADS  MathSciNet  Google Scholar 

  64. M.F. Sykes, D.S. Gaunt: J. Phys. A 9, 2131 (1976)

    ADS  Google Scholar 

  65. N. Ogita, A. Ueda, T. Matsubara, H. Matsuda, F. Yonezawa: J. Phys. Soc. Jpn. (Suppl.) 26, 145 (1969)

    ADS  Google Scholar 

  66. A. Sur, J. Lebowitz, J. Marro, M. Kalos: Phys. Rev. B 15, 3014 (1977)

    ADS  Google Scholar 

  67. T. Schneider, E. Stoll: In Anharmonic Lattices, Structural Transitions and Melting, ed. by T. Riste (Nordhoff, Leiden 1971) p. 275

    Google Scholar 

  68. K. Binder, H. Müller-Krumbhaar: Phys. Rev. B 9, 2328 (1974)

    ADS  Google Scholar 

  69. E. Stoll, K. Binder, T. Schneider: Phys. Rev. B 8, 3266 (1973)

    ADS  Google Scholar 

  70. P. Mirold, K. Binder: Acta Met. 25, 1435 (1977)

    Article  Google Scholar 

  71. H. Müller-Krumbhaar: Unpublished

    Google Scholar 

  72. E.P. Stoll, T. Schneider: Physica B 8688, 1419 (1977)

    Google Scholar 

  73. K. Kawasaki: In Ref. 5.50, Vol. II, p. 443

    Google Scholar 

  74. K. Binder, D. Stauffer: Advan. Phys. 25, 343 (1976)

    Article  ADS  Google Scholar 

  75. C. Domb: Ann. Israel Phys. Soc. 2, 225 (1978)

    Google Scholar 

  76. P.L. Leath, G.R. Reich: J. Phys. C 11, 4017 (1978)

    ADS  Google Scholar 

  77. W. Klein, H.E. Stanley, P.J. Reynolds, A. Coniglio: Phys. Rev. Lett. 41, 1145 (1978)

    Article  ADS  Google Scholar 

  78. S. Kirkpatrick: in Ill-Condensed Matter, ed. by R. Balian, R. Maynard, and G. Toulouse (North-Holland, Amsterdam 1979)

    Google Scholar 

  79. R.J. Reynolds, H.E. Stanley, W. Klein: J. Phys. A 11, 199 (1978)

    ADS  Google Scholar 

  80. J. Hoshen, R. Kopelman, E.M. Monberg: J. Statist. Phys. 19, 219 (1978)

    Article  ADS  Google Scholar 

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© 1986 Springer-Verlag Berlin Heidelberg

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Müller-Krumbhaar, H. (1986). Simulation of Small Systems. In: Binder, K. (eds) Monte Carlo Methods in Statistical Physics. Topics in Current Physics, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82803-4_5

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  • DOI: https://doi.org/10.1007/978-3-642-82803-4_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16514-9

  • Online ISBN: 978-3-642-82803-4

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