Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-25T15:22:50.503Z Has data issue: false hasContentIssue false

Modified Fisher Droplet Model

Published online by Cambridge University Press:  21 February 2011

J. Marro
Affiliation:
Departamento de Fĺsica Teórica, Universidad de Barcelona, Diagonal 647, Barcelona-28, Spain
R. Toral
Affiliation:
Departamento de Fĺsica Teórica, Universidad de Barcelona, Diagonal 647, Barcelona-28, Spain
Get access

Abstract

We propose a simple modification of the Fisher droplet model which, unlike classical nucleation theory, reproduces very well some Monte Carlo equilibrium cluster distributions P1 for the three-dimensional Ising or lattice gas model. It then follows that p1(h) /p1(h=0) = A exp(− η l) where η ∝hl/Y, y≃0.45, when the magnetic field h is small enough, as suggested from the consideration of an effective cluster size ly , while η seems rather proportional to h at larger values of the field, as implied by some exact results.

Type
Research Article
Copyright
Copyright © Materials Research Society 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Yang, C.N. and Lee, T.D., Phys. Rev. 87, 404, 410 (1952)Google Scholar
2. See, for instance, Thompson, C.J., Mathematical Statistical Mechanics (Princeton Univ. Press, Princeton 1972)Google Scholar
3. Becker, R. and Döring, W., Ann. Physik 24, 719 (1935)Google Scholar
4. Zettlemoyer, A.C. ed., Nucleation (Dekker, New York 1969) andGoogle Scholar
4a Nucleation Phenomena (Elsevier, Amsterdam 1977);Google Scholar
4b Binder, K. ed., Monte Carlo Methods in Statistical Physics (Springer-Verlag, Berlin 1979)Google Scholar
5. Fisher, M.E., Physics 3, 255 (1967)Google Scholar
6. Binder, K., Ann. Phys.(N.Y.) 98, 390 (1976)Google Scholar
7. Stauffer, D., Coniglio, A. and Heermann, D.W., Phys. Rev. Lett. (1982)Google Scholar
7a. and preprint; Stauffer, J. Kertész, D. and Coniglio, A., preprint for Ann. Israel Phys. Soc. (Perc. Vol.) (Adler et al editors)Google Scholar
8. Marro, J. and Toral, R., preprint 1983, and references therein.Google Scholar
9. Lebowitz, J.L. and Penrose, O., J. Stat. Phys. 16, 321 (1977)Google Scholar
10. Binder, K., Kalos, M., Lebowitz, J. and Marro, J., Adv. Colloid Interface Sci. 10, 173 (1979)Google Scholar
11. Marro, J. et al, preprint(1983)Google Scholar
12. Kunz, H. and B. Souillard, Phys. Rev. Lett. 40, 133 (1978);Google Scholar
12a J. Stat. Phys. 19, 77 (1978)Google Scholar
13. Essam, J.W. and Fisher, M.E., J. Chem. Phys. 38, 802 (1963)Google Scholar
14. Müller-Krumbhaar, H. and Stoll, E.P., J. Chem. Phys. 65, 4294 (1976)Google Scholar