Monte Carlo Study of the Critical Dynamics at the Surface of an Ising Model

  • P. A. Slotte
  • S. Wansleben
  • D. P. Landau
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 33)

Abstract

The model studied is the ferromagnetic 3D-Ising model on a simple cubic lattice with a free surface, i.e., the hamiltonian
$$ - \beta H = K\mathop \Sigma \limits_{ < ij > _{\text{b}} } {\text{s}}_{\text{i}} s_{\text{j}} + {\text{K}}_{\text{s}} \mathop \Sigma \limits_{ < {\text{ij}} > _{\text{s}} } {\text{s}}_{\text{i}} {\text{s}}_{\text{j}} ,{\text{ s}}_{\text{i}} = \pm 1,{\text{ }}(1)$$
(1)
where the second sum runs over spin pairs where both spins are in the surface, the first sum runs over all other nearest-neighbor spin pairs, and β = 1/kT, with k the Boltzmann constant and T temperature. The static properties of this model are well known [1–4]. For temperatures below the bulk critical temperature, Kc ≈ 0.221654 [5], both the surface and the bulk are ferromagnetically ordered. For strong surface coupling, i.e., ratios of the surface to bulk coupling, R = Ks/K, above a tricritical value, Rt ≈ 1.52 [2], the surface orders at a higher temperature than the bulk. We have studied the critical dynamics of the surface layer in this model at the ordinary transition (R = 1.0) and at the tricritical point (R = 1.52, also called the special transition).

Keywords

Autocorrelation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    K. Binder: In Phase Transitions and Critical Phenomena, ed. C. Domb and J. Lebowitz, Vol. 8 (Academic Press, London 1983).Google Scholar
  2. 2.
    K. Binder and D. P. Landau: Phys. Rev. Lett. 52, 318 (1984).ADSCrossRefGoogle Scholar
  3. 3.
    H. Diehl and S. Dietrich: Phys. Rev. B24, 2878 (1981).ADSGoogle Scholar
  4. 4.
    M. Kikuchi and Y. Okabe: Prog. Theor. Phys. 73, 32 (1985). Prog. Theor. Phys. 74, 458 (1985)ADSCrossRefGoogle Scholar
  5. Y. Okabe, M. Kikuchi and K. Ohno: Prog. Theor. Phys. 75, 496 (1986).ADSCrossRefGoogle Scholar
  6. 5.
    G. S. Pawley, R. H. Swendsen, D. J. Wallace and K.G. Wilson: Phys. Rev. B29, 4030 (1984).ADSGoogle Scholar
  7. 6.
    P. C. Hohenberg and B. I. Halperin: Mod. Phys. Rev. 49, 435 (1977).ADSCrossRefGoogle Scholar
  8. 7.
    S. Wansleben and D. P. Landau: J. Appl. Phys. 61, 3968 (1987).ADSCrossRefGoogle Scholar
  9. 8.
    S. Tang and D. P. Landau: Phys. Rev. 36, 567 (1987).ADSCrossRefGoogle Scholar
  10. 9.
    R. Bausch, V. Dohm, H. K. Janssen and R. K. P. Zia: Phys. Rev. Lett. 47, 1837 (1981).ADSCrossRefGoogle Scholar
  11. 10.
    J. C. LeGuillou and J. Zinn-Justin: Phys. Rev. B21, 3976 (1980).MathSciNetADSGoogle Scholar
  12. 11.
    S. Dietrich and H. W. Diehl: Z. Phys. B51, 343 (1983).ADSCrossRefGoogle Scholar
  13. 12.
    M. Kikuchi and Y. Okabe: Phys. Rev. Lett. 55, 1220 (1985).ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • P. A. Slotte
    • 1
  • S. Wansleben
    • 1
  • D. P. Landau
    • 1
  1. 1.Center for Simulational PhysicsUniversity of GeorgiaAthensUSA

Personalised recommendations