Journal of Statistical Physics

, Volume 36, Issue 3–4, pp 447–470 | Cite as

Nucleation and metastability in three-dimensional Ising models

  • Dieter W. Heermann
  • Antonio Coniglio
  • W. Klein
  • Dietrich Stauffer


We present Monte Carlo experiments on nucleation theory in the nearest-neighbor three-dimensional Ising model and in Ising models with long-range interactions. For the nearest-neighbor model, our results are compatible with the classical nucleation theory (CNT) for low temperatures, while for the long-range model a breakdown of the CNT was observed near the mean-field spinodal. A new droplet model and a zeroth-order theory of droplet growth are also presented.

Key words

Classical nucleation theory droplet definitions lattice gas Monte Carlo spinodal 


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  1. 1.
    R. Becker and W. Döring,Ann. Phys. (Leipzig) 24:719 (1935).Google Scholar
  2. 2.
    W. Döring,Z. Phys. Chem. 36:317 (1937).Google Scholar
  3. 3.
    B. Chu, F. J. Schoenes, and M. E. Fisher,Phys. Rev. 185, 185 (1969).Google Scholar
  4. 4.
    K. Binder,Ann. Phys. (N.Y.) 98:345 (1976).Google Scholar
  5. 5.
    J. D. Gunton, M. San Miguel, and P. S. Sahni, inPhase Transitions and Critical Phenomena, (C. Domb and J. L. Lebowitz, Eds.) (Academic press, London, 1983).Google Scholar
  6. 6.
    A. C. Zettlemoyer, ed.Nucleation I (Dekker, New York, 1969).Google Scholar
  7. 7.
    J. W. Cahn and J. Hilliard,J. Chem. Phys. 31:688 (1959).Google Scholar
  8. 8.
    K. Binder and D. Stauffer,Adv. Phys. 25:345 (1976).Google Scholar
  9. 9.
    K. Binder and E. Stoll,Phys. Rev. Lett. 31:47 (1973).Google Scholar
  10. 10.
    J. L. Lebowitz, J. Marro, and M. H. Kalos,Acta Metall. 30:297 (1982).Google Scholar
  11. 11.
    M. H. Kalos, J. L. Lebowitz, O. Penrose, and A. Sur,J. Stat. Phys. 18:39 (1978); O. Penrose, J. L. Lebowitz, J. Marro, M. H. Kalos, and A. Sur,ibid. 19:243 (1978); O. Penrose and A. Buhagior,ibid. 30:219 (1983).Google Scholar
  12. 11a.
    J. Marro and R. Toral,Physica, to be published.Google Scholar
  13. 12.
    A. Coniglio and W. Klein,J. Phys. A 13:2775 (1980).Google Scholar
  14. 13.
    H. Müller-Krumbhaar,Phys. Lett. 50A:27 (1975).Google Scholar
  15. 14.
    D. W. Heermann and D. Stauffer,Z. Phys. B 44:339 (1980).Google Scholar
  16. 15.
    Roussenq, A. Coniglio, and D. Stauffer,J. Phys. Lett. (1982).Google Scholar
  17. 16.
    J. Kertesz, D. Stauffer, and A. Coniglio,Ann. Israel Phys. Soc. 5:121 (1983).Google Scholar
  18. 17.
    D. Stauffer, A. Coniglio, and D. W. Heermann,Phys. Rev. Lett. 49:1299 (1984).Google Scholar
  19. 18.
    D. Stauffer,Phys. Rep. 54:1 (1979).Google Scholar
  20. 19.
    Reeve,J. Phys. A 15:L521 (1982).Google Scholar
  21. 20.
    K. Binder,Phys. Rev. A 25:1699 (1982).Google Scholar
  22. 21.
    H. Furukawa and K. Binder,Phys. Rev. A 26:556 (1982).Google Scholar
  23. 22.
    F. H. Stillinger, private communication.Google Scholar
  24. 23.
    J. D. Weeks, G. H. Gilmer, and H. J. Leamy,Phys. Rev. Lett. 31:549 (1973).Google Scholar
  25. 24.
    K. W. Kehr and K. Binder, inMonte Carlo Methods in Statistical Physics, Vol. II, edited by K. Binder (Springer, Berlin, 1984).Google Scholar
  26. 25.
    C. Comb and N. W. Dalton,Proc. Phys. Soc. 89:859 (1966).Google Scholar
  27. 26.
    D. W. Heermann, W. Klein, and D. Stauffer,Phys. Rev. Lett. 47:1262 (1982).Google Scholar
  28. 27.
    D. W. Heermann and W. Klein,Phys. Rev. B 27:1732 (1983).Google Scholar
  29. 28.
    C. Domb,Adv. Phys. 9:149 (1960).Google Scholar
  30. 29.
    A. Coniglio, H. E. Stanley, and W. Klein,Phys. Rev. B 25:6805 (1982).Google Scholar
  31. 30.
    W. Klein and C. Unger,Phys. Rev. B 28 (1983).Google Scholar
  32. 31.
    A. Coniglio and T. C. Lubensky,J. Phys. A13:1783 (1980).Google Scholar
  33. 32.
    P. A. Rikvold,Phys. Rev. A 26: 647 (1982).Google Scholar
  34. 33.
    B. B. Mandelbrot,Ann. Israel Phys. Soc. 5:59 (1983).Google Scholar
  35. 34.
    C. Unger and W. Klein,Phys. Rev. B 29:2698 (1984).Google Scholar
  36. 35.
    D. W. Heermann and W. Klein,Phys. Rev. B 27:1732 (1983).Google Scholar
  37. 36.
    D. W. Heermann and W. Klein,Phys. Rev. Lett. 50:1062 (1983).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • Dieter W. Heermann
    • 1
  • Antonio Coniglio
    • 1
  • W. Klein
    • 1
  • Dietrich Stauffer
    • 1
  1. 1.Center for Polymer Studies and Department of PhysicsBoston UniversityBoston

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