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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 Function Monte Carlo Study Finite Size Effect Tricritical Point Dynamical Exponent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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

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