Statistical investigation on the dynamic behaviors of maximal spatial persistence in saturated surfaces of discrete growth models

Abstract

The dynamic scaling behaviors of the maximal spatial persistence τmax in saturated surface of (1+1)-dimensional discrete growth models, including Wolf–Villain model, Family model, Ballistic Deposition model and Restricted Solid-on-Solid model, are investigated by means of Kinetic Monte Carlo method. Linear relationships are found for the mean value <τmax(L)>≈A⋅L, and the root-mean square deviation (i.e. the second moment) σ(L)≈B⋅L (where σ=(〈τmax2〉−〈τmax〉2)1∕2), respectively, versus the system size L. The distribution of the maximal spatial persistence is also analyzed, and data collapsing for different system sizes to a single curve implying good scaling behavior. It is shown that the distribution of maximal spatial persistence does not satisfy the commonly used extreme statistical distribution, namely Weibull and Gumbel distribution, but can better conform to Asym2Sig distribution.