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Random deposition model with surface relaxation in higher dimensions

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  • Kwak, Wooseop
  • Kim, Jin Min

Abstract

A random deposition model with surface relaxation, so-called the Family model is studied in higher dimensions. In three dimensions, the surface width W(t) characterizing the roughness of a surface grows as 2blogt at the beginning and becomes saturated at 2alogL for t≫Lz, where L is the system size. The dynamic exponent z=1.99(2) is estimated from the relation z=a∕b and a nice data collapse of the scaling plot W2(L,t)∼logL2agt∕Lz is given with z=2. In four dimensions, the surface width approaches an intrinsic width Wint with a small correction term W2(L,t)=Wint2−L2αft∕Lz, where z≈1.97 and negative exponent α≈−0.52 are obtained. Our results support that the Family model belongs to the Edwards–Wilkinson universality class even in higher dimensions.

Suggested Citation

  • Kwak, Wooseop & Kim, Jin Min, 2019. "Random deposition model with surface relaxation in higher dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 87-92.
    • Handle: RePEc:eee:phsmap:v:520:y:2019:i:c:p:87-92
    DOI: 10.1016/j.physa.2019.01.016
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    References listed on IDEAS

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    1. Family, Fereydoon, 1990. "Dynamic scaling and phase transitions in interface growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(1), pages 561-580.
    2. Aarão Reis, F.D.A., 2002. "Relaxation to steady states and dynamical exponents in deposition models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 250-258.
    3. Kim, Jin Min & Lee, Jae Hwan & Kim, In-mook & Yang, Jin & Lee, Youngki, 2000. "Relaxation function and dynamic exponent for discrete growth models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(3), pages 304-311.
    4. Pal, S & Landau, D.P, 1999. "The Edwards–Wilkinson model revisited: large-scale simulations of dynamic scaling in 2+1 dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 267(3), pages 406-413.
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    Cited by:

    1. Mallio, Daniel O. & Aarão Reis, Fábio D.A., 2022. "Short length scale fluctuations in lattice growth models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    2. Lebovka, Nikolai I. & Cieśla, Michał & Vygornitskii, Nikolai V., 2024. "Sedimentation of a suspension of discorectangles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 644(C).

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