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Finite-size effects on the growth models of Das Sarma and Tamborenea and Wolf and Villain

Author

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  • Costa, B.S.
  • Euzébio, J.A.R.
  • Aarão Reis, F.D.A.

Abstract

The original versions of the limited-mobility growth models of Das Sarma and Tamborenea (DT) and of Wolf and Villain (WV) were simulated in one-dimensional substrates of lengths L⩽256 and ⩽512, respectively. The growth regime may be separated in two regions, giving effective growth exponents βL. Finite-size estimates of the roughness exponent, αL, and of the dynamical exponents, zL, are obtained from data in the steady states. The behavior of the effective exponents rules out the description by the fourth-order linear theory of interface growth in the continuum limit. For the DT model, βL shows a crossover to β≈13 and extrapolations of αL considering finite-size corrections with the local roughness exponent give α≈1, both consistent with the fourth-order nonlinear theory, while zL shows a slower crossover. For the WV model, extrapolations of αL and zL are consistent with the values of the Edwards–Wilkinson theory, α=0.5 and z=2. These results improve previous ones for the original DT and WV models, from which we conclude that, considering certain systematic data extrapolation methods, the theoretically predicted universality classes can be inferred without using noise reduction schemes.

Suggested Citation

  • Costa, B.S. & Euzébio, J.A.R. & Aarão Reis, F.D.A., 2003. "Finite-size effects on the growth models of Das Sarma and Tamborenea and Wolf and Villain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(1), pages 193-204.
    • Handle: RePEc:eee:phsmap:v:328:y:2003:i:1:p:193-204
    DOI: 10.1016/S0378-4371(03)00581-8
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    Cited by:

    1. Disrattakit, P. & Chanphana, R. & Chatraphorn, P., 2016. "Roughness distribution of multiple hit and long surface diffusion length noise reduced discrete growth models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 619-629.
    2. Disrattakit, P. & Chanphana, R. & Chatraphorn, P., 2017. "Skewness and kurtosis of height distribution of thin films simulated by larger curvature model with noise reduction techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 299-308.

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