Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Becker and W. Döring,Ann. Phys. (Leipzig) 24:719 (1935).
W. Döring,Z. Phys. Chem. 36:317 (1937).
B. Chu, F. J. Schoenes, and M. E. Fisher,Phys. Rev. 185, 185 (1969).
K. Binder,Ann. Phys. (N.Y.) 98:345 (1976).
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).
A. C. Zettlemoyer, ed.Nucleation I (Dekker, New York, 1969).
J. W. Cahn and J. Hilliard,J. Chem. Phys. 31:688 (1959).
K. Binder and D. Stauffer,Adv. Phys. 25:345 (1976).
K. Binder and E. Stoll,Phys. Rev. Lett. 31:47 (1973).
J. L. Lebowitz, J. Marro, and M. H. Kalos,Acta Metall. 30:297 (1982).
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).
J. Marro and R. Toral,Physica, to be published.
A. Coniglio and W. Klein,J. Phys. A 13:2775 (1980).
H. Müller-Krumbhaar,Phys. Lett. 50A:27 (1975).
D. W. Heermann and D. Stauffer,Z. Phys. B 44:339 (1980).
Roussenq, A. Coniglio, and D. Stauffer,J. Phys. Lett. (1982).
J. Kertesz, D. Stauffer, and A. Coniglio,Ann. Israel Phys. Soc. 5:121 (1983).
D. Stauffer, A. Coniglio, and D. W. Heermann,Phys. Rev. Lett. 49:1299 (1984).
D. Stauffer,Phys. Rep. 54:1 (1979).
Reeve,J. Phys. A 15:L521 (1982).
K. Binder,Phys. Rev. A 25:1699 (1982).
H. Furukawa and K. Binder,Phys. Rev. A 26:556 (1982).
F. H. Stillinger, private communication.
J. D. Weeks, G. H. Gilmer, and H. J. Leamy,Phys. Rev. Lett. 31:549 (1973).
K. W. Kehr and K. Binder, inMonte Carlo Methods in Statistical Physics, Vol. II, edited by K. Binder (Springer, Berlin, 1984).
C. Comb and N. W. Dalton,Proc. Phys. Soc. 89:859 (1966).
D. W. Heermann, W. Klein, and D. Stauffer,Phys. Rev. Lett. 47:1262 (1982).
D. W. Heermann and W. Klein,Phys. Rev. B 27:1732 (1983).
C. Domb,Adv. Phys. 9:149 (1960).
A. Coniglio, H. E. Stanley, and W. Klein,Phys. Rev. B 25:6805 (1982).
W. Klein and C. Unger,Phys. Rev. B 28 (1983).
A. Coniglio and T. C. Lubensky,J. Phys. A13:1783 (1980).
P. A. Rikvold,Phys. Rev. A 26: 647 (1982).
B. B. Mandelbrot,Ann. Israel Phys. Soc. 5:59 (1983).
C. Unger and W. Klein,Phys. Rev. B 29:2698 (1984).
D. W. Heermann and W. Klein,Phys. Rev. B 27:1732 (1983).
D. W. Heermann and W. Klein,Phys. Rev. Lett. 50:1062 (1983).
Author information
Authors and Affiliations
Additional information
Supported in part by grants from ARO, ONR, and NSF.
Rights and permissions
About this article
Cite this article
Heermann, D.W., Coniglio, A., Klein, W. et al. Nucleation and metastability in three-dimensional Ising models. J Stat Phys 36, 447–470 (1984). https://doi.org/10.1007/BF01010991
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01010991