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Dynamic scaling and phase transitions in interface growth

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  • Family, Fereydoon

Abstract

The dynamic scaling approach is an effective tool for understanding the temporal evolution of fluctuating interfaces. The surface width w obeys the scaling form w(L, t)=Lαƒ(t/Lαβ, where α and β are exponents which characterize how the surface width grows with the length scale L and the time t. Applications of dynamic scaling to a number of surface growth models are discussed. The results of a large-scale simulation of the ballistic deposition model in three dimensions are presented and compared with recent conjectures. The question of universality in interface growth is addressed and a finite temperature generalization of the restricted solid-on-solid model is studied. This model appears to undergo a phase transition from the usual rough phase at high temperatures to a new phase at low temperatures. Numerical solutions of the generalized Langevin equation indicate that there is no phase transition in 2+1 dimensions. Thus, the relation between the continuum equation and the discrete models is still an open question.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:168:y:1990:i:1:p:561-580
    DOI: 10.1016/0378-4371(90)90409-L
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    Cited by:

    1. Socoteanu, Radu & Anastasescu, Mihai & Dobrescu, Gianina & Boscencu, Rica & Vasiliu, Georgiana & Constantin, Carolina, 2015. "AFM imaging, fractal analysis and in vitro cytotoxicity evaluation of Zn(II) vs. Cu(II) porphyrins," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 304-309.
    2. 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.

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