Skip to main content

Simulations of Phase Transitions in Confined Geometry

  • Chapter
Computer Simulations of Surfaces and Interfaces

Part of the book series: NATO Science Series ((NAII,volume 114))

  • 525 Accesses

Abstract

We review Monte Carlo simulations of ferromagnetic Ising lattices in a film geometry with surface magnetic fields. The resultant behavior may be critical, 1st order, or tricritical wetting, interface localization-delocalization, and capillary condensation depending upon the film thickness and the boundary conditions used. In a different set of circumstances, an Ising lattice gas model may be used to study growth of MBE films where both deposition and diffusion are allowed. Here the difference between Monte Carlo and kinetic Monte Carlo is important.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. For a detailed review of both the theory and Monte Carlo simulations see: K. Binder. D. P. Landau, and M. Müller, J. Stat. Phys. (in press).

    Google Scholar 

  2. H. Nakanishi and M. E. Fisher, Phys. Rev. Lett. 49: 1565 (1982)

    Article  ADS  Google Scholar 

  3. K. Binder and P. C. Hohenberg, Phys. Rev. B6: 3461 (1972); ibid B9: 2194 (1974).

    Article  ADS  Google Scholar 

  4. K. Binder, in Phase Transitions and Critical Phenomena, Vol VIII, C. Domb and J. L. Lebowitz, eds. (Academic, New York, 1983) p. 1.

    Google Scholar 

  5. Near the roughening transition temperature T R complete wetting is replaced by a sequence of layering transitions. See Ref. [6].

    Google Scholar 

  6. K. Binder and D. P. Landau, Phys. Rev. B46: 4844 (1992).

    ADS  Google Scholar 

  7. K. Binder, R. Evans, D. P. Landau, and A. M. Ferrenberg, Phys. Rev. E53: 5023 (1996).

    ADS  Google Scholar 

  8. A. O. Parry and R. Evans, Phys. Rev. Lett. 64: 439 (1990).

    Article  ADS  Google Scholar 

  9. A. O. Parry and R. Evans, Physica A181: 250 (1992).

    ADS  Google Scholar 

  10. M. E. Fisher and H. Nakanishi, J. Chem. Phys. 75: 5857 (1981).

    Article  ADS  Google Scholar 

  11. H. Nakanishi and M. E. Fisher, J. Chem. Phys. 78: 3279 (1983).

    Article  ADS  Google Scholar 

  12. E. Brezin, B. I. Halperin, and S. Leibler, Phys. Rev. Lett. 50: 1387 (1983).

    Article  ADS  Google Scholar 

  13. R. Lipowsky, D. M. Kroll, and R. K. P. Zia, Phys. Rev. B 27: 4499 (1983).

    Article  ADS  Google Scholar 

  14. D. S. Fisher and D. A. Huse, Phys. Rev. B32: 247 (1985).

    ADS  Google Scholar 

  15. R. Lipowsky and M. E. Fisher, Phys. Rev. B36: 2126 (1987).

    MathSciNet  ADS  Google Scholar 

  16. M. E. Fisher and H. Wen, Phys. Rev. Lett. 68: 3654 (1992).

    Article  ADS  Google Scholar 

  17. D. P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge, 2000).

    MATH  Google Scholar 

  18. K. Binder and D. P. Landau, J. Appl. Phys. 57: 3306 (1985).

    Article  ADS  Google Scholar 

  19. K. Binder, D. P. Landau, and D. M. Kroll, Phys. Rev. Lett. 56, 2276 (1986).

    Article  ADS  Google Scholar 

  20. K. Binder and D. P. Landau, Phys. Rev. B37: 1745 (1988).

    Article  ADS  Google Scholar 

  21. K. Binder, D. P. Landau, and S. Wansleben, Phys. Rev. B40: 6971 (1989).

    ADS  Google Scholar 

  22. E. Brézin and T. Halpin-Healey, Phys. Rev. Lett. 58: 1220. (1987).

    Article  ADS  Google Scholar 

  23. A. O. Parry and C. J. Boulter, Phys. Rev. E53: 6577 (1996).

    ADS  Google Scholar 

  24. M. E. Fisher and A. J. Jin, Phys. Rev. Lett. 69: 792 (1992); A. J. Jin and M. E. Fisher, Phys. Rev. B47: 7365 (1993).

    Article  ADS  Google Scholar 

  25. C. J. Boulter and A. O. Parry, Phys. Rev. Lett. 74: 3403 (1995).

    Article  ADS  Google Scholar 

  26. D. Ross, D. Bonn and J. Meunier, Nature 400: 737 (1999); and (to be published).

    Article  ADS  Google Scholar 

  27. K. Binder and D. P. Landau, Phys. Rev. Lett. 52: 318 (1984).

    Article  ADS  Google Scholar 

  28. D. P. Landau and K. Binder, Phys. Rev. B41: 4633 (1990).

    Article  ADS  Google Scholar 

  29. C. Ruge, S. Dunkelmann, F. Wagner, and J. Wulf, J. Stat. Phys. 73: 293 (1993).

    Article  ADS  MATH  Google Scholar 

  30. C. Ruge and F. Wagner, Phys. Rev. B52: 4209 (1995).

    ADS  Google Scholar 

  31. K. Binder and D. P. Landau, J. Chem. Phys. 96: 1444 (1992).

    Article  ADS  Google Scholar 

  32. A. J. Liu and M. E. Fisher, Physica A156: 35 (1989).

    MathSciNet  ADS  Google Scholar 

  33. A. O. Parry and C. J. Boulter, Physica A218: 77 (1995).

    ADS  Google Scholar 

  34. C. J. Boulter and A. O. Parry, Physica A218: 109 (1995).

    ADS  Google Scholar 

  35. A. O. Parry, C. J. Boulter and P. S. Swain, Phys. Rev. E52: R5768 (1995).

    Google Scholar 

  36. P. S. Swain and A. O. Parry, Europhys. Lett. 37: 207 (1997).

    Article  ADS  Google Scholar 

  37. A. O. Parry, J. Phys.: Condens. Matter 8: 10761 (1996).

    Article  ADS  Google Scholar 

  38. K. Binder, D. P. Landau, and A. M. Ferrenberg, Phys. Rev. Lett. 74: 298 (1995).

    Article  ADS  Google Scholar 

  39. K. Binder, D. P. Landau, and A. M. Ferrenberg, Phys. Rev. E51: 2823 (1995).

    ADS  Google Scholar 

  40. A. M. Ferrenberg, D. P. Landau and K. Binder, Phys. Rev. E58: 3353 (1998).

    Article  ADS  Google Scholar 

  41. S. Pal and D. P. Landau, Phys. Rev. E 49, 10,597 (1994).

    Google Scholar 

  42. P. Smilauer and D. D. Vvedensky, Phys. Rev. B 48, 17,603 (1993).

    Article  ADS  Google Scholar 

  43. S. Pal and D. P. Landau, Physica A 267, 406 (1999).

    Article  Google Scholar 

  44. Y. Shim, D. P. Landau, and S. Pal, Phys. Rev. E 58, 7571 (1998).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Landau, D.P. (2003). Simulations of Phase Transitions in Confined Geometry. In: Dünweg, B., Landau, D.P., Milchev, A.I. (eds) Computer Simulations of Surfaces and Interfaces. NATO Science Series, vol 114. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0173-1_14

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-0173-1_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1464-2

  • Online ISBN: 978-94-010-0173-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics