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Relaxation function and dynamic exponent for discrete growth models

Author

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  • Kim, Jin Min
  • Lee, Jae Hwan
  • Kim, In-mook
  • Yang, Jin
  • Lee, Youngki

Abstract

We develop a new method of measuring the dynamic exponent z for discrete growth models. Starting from a sinusoidal initial surface of a selected wavelength l, we consider a relaxation function R(t,l), which is a quantity similar to the autocorrelation function of the surface height. Typically the relaxation function decays exponentially following ∼e−g(t/τ(l)), where τ(l) is the relaxation time and it depends on the wavelength l. The dynamic exponent z is measured by the relation τ(l)∼lz. We find that g(x) scales as x1.0 for the Family model and as x1.5 for the restricted solid-on-solid model. The advantages of the method are also discussed.

Suggested Citation

  • Kim, Jin Min & Lee, Jae Hwan & Kim, In-mook & Yang, Jin & Lee, Youngki, 2000. "Relaxation function and dynamic exponent for discrete growth models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(3), pages 304-311.
    • Handle: RePEc:eee:phsmap:v:278:y:2000:i:3:p:304-311
    DOI: 10.1016/S0378-4371(99)00595-6
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    Cited by:

    1. 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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