Abstract
We discuss the results of extensive numerical simulations in order to estimate the scaling exponents associated with kinetic roughening in higher dimensions, up tod=7 + l. To this end, we study the restricted solid-on-solid growth model, for which we employ a novel fitting ansatz for the spatially averaged height correlation function¯G(t)∼t 2β to estimate the scaling exponentβ. Using this method, we present a quantitative determination ofβ ind=3 + 1 and 4+1 dimensions. To check the consistency of these results, we also compute the interface width and determineβ andx from it independently. Our results are in disagreement with all existing theories and conjectures, but in four dimensions they are in good agreement with recent simulations of Forrest and Tang for a different growth model. Above five dimensions, we use the time dependence of the width to obtain lower bound estimates forβ. Within the accuracy of our data, we find no indication of an upper critical dimension up tod = 7 + 1.
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References
J. Krug and H. Spohn, inSolids far from Equilibrium: Growth, Morphology and Defects, C. Godreche ed. (Cambridge University Press, Cambridge, 1991).
D. Forster, D. R. Nelson, and J. M. Stephen,Phys. Rev. A 16:732 (1977).
J. Koplik and H. Levine,Phys. Rev. B 32:280 (1985).
M. Kardar, G. Parisi, and Y. C. Zhang,Phys. Rev. Lett. 56:889 (1986).
J. Villain,J. Phys. (Paris)I 1:19 (1991).
M. Kardar and Y.-C. Zhang,Phys. Rev. Lett. 58:2087 (1987).
T. Hwa,Phys. Rev. Lett. 69:1552 (1992).
E. Medina, T. Hwa, M. Kardar, and Y.-C, Zhang,Phys. Rev. A 39:2053 (1989).
B. M. Forrest and L.-H. Tang,Phys. Rev. Lett. 64:1405 (1990); L.-H. Tang, B. M. Forrest, and D. E. Wolf,Phys. Rev. A 45:7162 (1992).
F. Family and T. Vicsek,J. Phys. A 18:L57 (1985).
A. Chakrabarti and R. Toral,Phys. Rev. A 40:11419 (1989); J. G. Amar and F. Family,Phys. Rev. A 41:3399 (1990); K.Moscr, D. E. Wolf, and J. Kertész,Physica A 178:215 (1991); B. M. Forrest and R. Toral, preprint (1992).
H. Guo, B. Grossmann, and M. Grant,Phys. Rev. Lett. 64:1262 (1990); H. Guo, B. Grossmann, and M. Grant,Phys. Rev. A 41:7082 (1990).
J. Krug and H. Spohn,Phys. Rev. Lett. 64:2332 (1990); J. M. Kim, T. Ala-Nissila, and J. M. Kosterlitz,Phys. Rev. Lett. 64:2333 (1990); D. A. Huse, J. G. Amar, and F. Family,Phys. Rev. A 41:7075 (1990).
J. M. Kim and J. M. Kosterlitz,Phys. Rev. Lett. 62:2289 (1989); J. M. Kim, J. M. Kosterlitz, and T. Ala-Nissila,J. Phys. A 24:5569 (1991).
T. Ala-Nissila, T. Hjelt, and J. M. Kosterlitz,Europhys. Lett. 19(1):1 (1992).
T. Hwa and E. Frey,Phys. Rev. A 44:R7873 (1991).
J. Krug, P. Meakin, and T. Halpin-Healy,Phys. Rev. A 45:638 (1992).
J. G. Amar and F. Family,Phys. Rev. A 45:5378 (1992).
L.-H. Tang,J. Stat. Phys. 67:819 (1992).
S. F. Edwards and D. R. Wilkinson,Proc. R. Soc. Lond. A 381:17 (1982).
T. Hwa, M. Kardar, and M. Paczuski,Phys. Rev. Lett. 66:441 (1991); S. T. Chui and J. D. Weeks,Phys. Rev. B 14:4978 (1976); P. Noziéres and F. Gallet,J. Phys. (Paris)48:353 (1987).
C. A. Doty and J. M. Kosterlitz,Phys. Rev. Lett. 69:1979 (1992).
T. Halpin-Healy,Phys. Rev. Lett. 62:442 (1989); T. Halpin-Healy,Phys. Rev. A 42:711 (1990).
J. Cook and B. Derrida,Europhys. Lett. 10:195 (1989); J. Cook and B. Derrida,J. Phys. A 23:1523 (1990).
H. G. E. Hentschel and F. Family,Phys. Rev. Lett. 66:1982 (1991).
W. Renz, private communication (1989).
J. M. Kim, M. A. Moore, and A. J. Bray,Phys. Rev. A 44:2345 (1991).
J. Krug and P. Meakin,J. Phys. A 23:L987 (1990).
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Ala-Nissila, T., Hjelt, T., Kosterlitz, J.M. et al. Scaling exponents for kinetic roughening in higher dimensions. J Stat Phys 72, 207–225 (1993). https://doi.org/10.1007/BF01048047
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DOI: https://doi.org/10.1007/BF01048047