Relaxation function and dynamic exponent for discrete growth models

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

Physica A: Statistical Mechanics and its Applications, 2000, vol. 278, issue 3, 304-311

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.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:278:y:2000:i:3:p:304-311

DOI: 10.1016/S0378-4371(99)00595-6

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