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Phys. Rev. A 43, 5275–5283 (1991)

[Issue 10 – 15 May 1991 ]

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Scaling properties of driven interfaces: Symmetries, conservation laws, and the role of constraints

Z. Rácz, M. Siegert, D. Liu, and M. Plischke

Physics Department, Simon Fraser University, Burnaby, British Columbia, Canada V5A||1S6

One-dimensional models of surface dynamics are studied analytically and by numerical simulation. In all cases the number of particles that form the deposit is conserved. We find that an initially flat surface, in general, roughens as a function of time and can be characterized by a width xi which obeys the scaling form xi (L,t)=L ^chi f(t/L^z) for a deposit on a substrate of linear dimension L. Restricted solid-on-solid (RSOS) -type models in which the microscopic dynamics obeys detailed balance are shown to be in the ``free-field'' universality class with exponents z=4 and chi =1/2. On the other hand, if detailed balance is broken, several universality classes exist. As the ``maximum-height-difference'' constraint in a RSOS model is varied, one can observe a phase transition between a flat phase (z=2, chi =0) and a grooved phase characterized by a steady-state exponent chi =1 but with no scaling in the relaxation process. At the transition point, a nontrivially rough surface emerges with exponents (z [approx equals] 3.67, chi [approx equals] 0.33) close to those of the conserved Kardar-Parisi-Zhang equation. We propose a phenomenological model that may account for these observations.

©1991 The American Physical Society

URL: http://link.aps.org/abstract/PRA/v43/p5275
DOI: 10.1103/PhysRevA.43.5275
PACS: 05.70.Ln, 05.40.+j, 68.35.Fx, 64.60.Ht

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References

1. F. Family and T. Vicsek, J. Phys. A 18, L75 (1985).
2. M. Plischke and Z. Rácz, Phys. Rev. A 32, 3825 (1985).
3. R. Jullien and R. Botet, Phys. Rev. Lett. 54, 2055 (1985).
4. F. Family, J. Phys. A 19, L441 (1986) [ INSPEC].
5. P. Meakin, P. Ramanlal, L. M. Sander and R. C. Ball, Phys. Rev. A 34, 5081 (1986).
6. M. Plischke, D. Liu and Z. Rácz, Phys. Rev. B 35, 3485 (1987).
7. D. E. Wolf and J. Kertesz, Europhys. Lett. 4, 651 (1987) [ INSPEC].
8. D. Liu and M. Plischke, Phys. Rev. B 38, 4781 (1988).
9. J. M. Kim and J. M. Kosterlitz, Phys. Rev. Lett. 62, 2289 (1989).
10. J. Krug, J. Phys. A 22, L769 (1989) [ INSPEC].
11. J. G. Amar and F. Family, Phys. Rev. Lett. 64, 543 (1990).
12. Y. P. Pellegrini and R. Jullien, Phys. Rev. Lett. 64, 1745 (1990).
13. B. M. Forrest and L-H. Tang, Phys. Rev. Lett. 64, 1405 (1990).
14. M. Kardar, G. Parisi and Y-C. Zhang, Phys. Rev. Lett. 56, 889 (1986) [SPIRES].
15. J. Krug, Phys. Rev. A 36, 5465 (1987).
16. H. Guo, B. Grossmann and M. Grant, Phys. Rev. Lett. 64, 1262 (1990).
17. T. Sun, H. Guo and M. Grant, Phys. Rev. A 40, 6763 (1989).
18. A. Chakrabarti, J. Phys. A 23, L919 (1990) [ INSPEC].
19. H. Guo and M. Grant (private communication).
20. A. De Masi, P. A. Ferrari and J. L. Lebowitz, Phys. Rev. Lett. 55, 1947 (1985).
21. It should be noted that this assumption does not exclude induced currents within the interface. These would be described by odd powers in the function f ( sigma _i).
22. P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977) [SPIRES]; Note that del² in Eq. (15) should, in principle, be replaced by a more general form that takes into account the fact that the particles move on an interface. The additional nonlinear terms do not, however, affect our conclusion that the Laplacian term is absent in (15).
23. L. Golubovic and R. Bruinsma, Phys. Rev. Lett. 66, 321 (1991).
24. A. Mazor, D. J. Srolovitz, P. S. Hagan and B. G. Bukiet, Phys. Rev. Lett. 60, 424 (1988); J. Villain, J. Phys. I (France) 1, 19 (1991) [ INSPEC].

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