Journal of the Korean Physical Society

, Volume 72, Issue 6, pp 699–702 | Cite as

A Conserved Current Solid-on-Solid Model on a Sierpinski Tetrahedron Substrate

  • Jin Min Kim
  • Daeseung Kang


A conserved current solid-on-solid model with conservative noise on a 3D Sierpinski tetrahedron substrate is studied. The interface width W grows as t β , with β = 0.0396 ± 0.0009, and becomes saturated as Lα, with α = 0.195±0.005, where L is the system size. The dynamic exponent z ≈ 4.92 is estimated from the relation z = α/β. These values satisfy a scaling relation α+z = 2z rw , where z rw is the random walk exponent of the fractal substrate. Our results are consistent with the values estimated from a fractional Langevin equation with a conservative noise.


Conserved current solid on solid model Conservative noise Fractal growth 


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  1. [1]
    F. Famil and T. Vicsek, Dynamics of Fractal Surfaces (World Scientific, ingapore, 1991).CrossRefGoogle Scholar
  2. [2]
    A-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995).CrossRefzbMATHGoogle Scholar
  3. [3]
    D. Huse and C. L. Henley, Phys. Rev. Lett. 54, 2708 (1985).ADSCrossRefGoogle Scholar
  4. [4]
    Molecular Beam Epitaxy and Heterostructures, edited by L. L. Chang and K. Ploog (Martinus Nijhoff, Dordrecht, 1985).Google Scholar
  5. [5]
    M. Kardar, G. Parisi and Y. C. Zhang, Phys. Rev. Lett. 56, 889 (1986).ADSCrossRefGoogle Scholar
  6. [6]
    F. Family and T. Vicsek, J. Phys. A 18, L75 (1985).ADSCrossRefGoogle Scholar
  7. [7]
    J. M. Kim and J. M. Kosterlitz, Phys. Rev. Lett. 62, 2289 (1989).ADSCrossRefGoogle Scholar
  8. [8]
    D. H. Kim and J. M. Kim, J. Stat Mech., P08008 (2010).Google Scholar
  9. [9]
    J. H. Lee, D. H. Kim and J. M. Kim, J. Korean Phys. Soc. 53, 1797 (2008).ADSCrossRefGoogle Scholar
  10. [10]
    T. Sun, H. Guo and M. Grant, Phys. Rev. A 40, 6763 (1989).ADSCrossRefGoogle Scholar
  11. [11]
    S. B. Lee, H-C. Jeong and J. M. Kim, J. Stat. Mech., P12013 (2008).Google Scholar
  12. [12]
    S. B. Lee and J. M. Kim, Phys. Rev. E 80, 021101 (2009).ADSCrossRefGoogle Scholar
  13. [13]
    G. Poupart and G. Zumofen, Phys. Rev. E 50, R663 (1994).ADSCrossRefGoogle Scholar
  14. [14]
    D. H. Kim and J. M. Kim, Phys. Rev. E. 84, 011105 (2011).ADSCrossRefGoogle Scholar
  15. [15]
    G. Tang, Z. Xun, R. Wen, K. Han, H. Xia, D. Hao, W. Zhou, X. Yanga and Y. Chen, Physica A 389, 4552 (2010).ADSCrossRefGoogle Scholar
  16. [16]
    C. M. Horowitz, F. Romá and E. V. Albano, Phys. Rev. E 78, 061118 (2008).ADSCrossRefGoogle Scholar
  17. [17]
    S. B. Lee, H-C. Jeong and J. M. Kim, J. Korean Phys. Soc. 58, 1076 (2011).ADSCrossRefGoogle Scholar
  18. [18]
    G. Zumofen, J. Klafter and A. Blumen, Phys. Rev. A 45, 8977 (1992).ADSCrossRefGoogle Scholar
  19. [19]
    J. Krug, Adv. Phys. 46, 139 (1997).ADSCrossRefGoogle Scholar
  20. [20]
    D. H. Kim and J. M. Kim, J. Stat. Mech., P09012 (2012).Google Scholar
  21. [21]
    S. Havlin and D. B. Avraham, Adv. Phys. 51, 187 (2002).ADSCrossRefGoogle Scholar

Copyright information

© The Korean Physical Society 2018

Authors and Affiliations

  1. 1.Department of PhysicsSoongsil UniversitySeoulKorea
  2. 2.Department of Electrical EngineeringSoongsil UniversitySeoulKorea

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