Relaxation to steady states and dynamical exponents in deposition models
Abstract
Considering some deposition models with limited mobility, we show that the typical decay of the interface width to its saturation value is exponential, which defines the crossover or saturation time \tau. We present a method to calculate a characteristic time \tau_0 proportional to \tau and estimate the dynamical exponent z. In one dimensional substrates of lengths L <~ 2048, the method is applied to the Family model, the restricted solidonsolid (RSOS) model and the ballistic deposition. Effective exponents z_L converge to asymptotic values consistent with the corresponding continuum theories. For the twodimensional Family model, the expected dynamic scaling hypothesis suggests a particular definition of \tau_0 that leads to z=2, improving previous calculations based on data collapse methods. For the twodimensional RSOS model, we obtain z ~ 1.6 and \alpha < 0.4, in agreement with recent large scale simulations.
 Publication:

arXiv eprints
 Pub Date:
 July 2002
 arXiv:
 arXiv:condmat/0207088
 Bibcode:
 2002cond.mat..7088A
 Keywords:

 Statistical Mechanics
 EPrint:
 5 pages, 6 figures, to be published in Physica A