Universality and corrections to scaling in the ballistic deposition model

F. D. A. Aarão Reis

doi:10.1103/PhysRevE.63.056116

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Universality and corrections to scaling in the ballistic deposition model

F. D. A. Aarão Reis

Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340 Niterói Rio de Janeiro, Brazil

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Phys. Rev. E 63, 056116 – Published 20 April, 2001

DOI: https://doi.org/10.1103/PhysRevE.63.056116

Abstract

In order to analyze some controversies on the equivalence between ballistic deposition (BD) and the Kardar-Parisi-Zhang (KPZ) theory, we simulated the BD model in one and two dimensions. Effective exponents $β_{L}$ were obtained in the growth regions, which were rigorously determined for various lengths L. Effective exponents $α_{L}$ were obtained from saturation widths in the steady-state regimes. In $d = 1$ we found $β_{L} = β {+ A L}^{- λ}$ and $α_{L} = α {+ B L}^{- Δ},$ with asymptotic exponents consistent with the KPZ values $β = 1 / 3$ and $α = 1 / 2,$ and correction-to-scaling exponents $0.2 ≲ λ ≲ 0.4$ and $0.6 ≲ Δ ≲ 0.8.$ These strong finite-size corrections explain the previous discrepancies between numerical estimates for BD and the exact KPZ results. In $d = 2$ we could only obtain reliable estimates of $α_{L},$ which are consistent with KPZ values if finite-size corrections with $Δ \approx 0.4$ are considered.

References (19)

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[c2] V. P. Zhdanov and P. R. Norton, Surf. Sci. 459, 245 (2000).

[c3] H. F. El-Nashar and H. A. Cerdeira, Phys. Rev. E 61, 6149 (2000).

[c4] Y. Shapir, S. Raychaudhuri, D. G. Foster, and J. Jorne, Phys. Rev. Lett. 84, 3029 (2000).

[c5] M. J. Vold, J. Colloid Sci. 14, 168 (1959); J. Phys. Chem. 63, 1608 (1959).

[c6] F. Family and T. Vicsek, J. Phys. A 18, L75 (1985).

[c7] M. Kardar, G. Parisi, and Y.-C. Zhang, Phys. Rev. Lett. 56, 889 (1986).

[c8] J. G. Amar and F. Family, Phys. Rev. A 41, 3399 (1990).

[c9] K. Moser, J. Kertész, and D. E. Wolf, Physica A 178, 215 (1991).

[c10] M. Lässig, Phys. Rev. Lett. 80, 2366 (1998).

[c11] J. M. Kim and J. M. Kosterlitz, Phys. Rev. Lett. 62, 2289 (1989).

[c12] T. Nagatani, Phys. Rev. E 58, 700 (1998).

[c13] P. Meakin, P. Ramanlal, L. M. Sander, and R. C. Ball, Phys. Rev. A 34, 5091 (1986).

[c14] P. Meakin, Phys. Rep. 235, 189 (1993).

[c15] R. M. D’Souza, Int. J. Mod. Phys. C 8, 941 (1997).

[c16] T. Halpin-Healy and Y.-C. Zhang, Phys. Rep. 254, 215 (1995).

[c17] R. M. D’Souza, Y. Bar-Yam, and M. Kardar, Phys. Rev. E 57, 5044 (1998).

[c18] E. Marinari, A. Pagnani, and G. Parisi, J. Phys. A 33, 8181 (2000).

[c19] R. Baiod, D. Kessler, P. Ramanlal, L. Sander, and R. Savit, Phys. Rev. A 38, 3672 (1988).

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Universality and corrections to scaling in the ballistic deposition model

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