Analyzing asymmetry in the Wolf-Villain model via the study of the persistence of various initial height fluctuations

Abstract

The Wolf-Villain (WV) model, which, in some literature, has shown trait of up-down asymmetry, is investigated through the study of the persistence probability of height fluctuations in simulated film surfaces. The persistence probability is the probability that the height fluctuation of each site does not cross its initial value (h 0) along a time interval. When averaged over all possible values of h 0, the probability is known to exhibit a power law decay behavior with the exponent called persistence exponent. In this work, instead of averaging over all h 0, we consider a fixed value of h 0 and find that the persistence probability of the WV model still decreases with time as a power law if the fixed value meets a necessary condition, i.e. h 0 is roughly equal to or larger than the saturated roughness of the film. The persistence exponent for each h 0 is measured and found to decrease as the value of h 0 increases. Scaling form of the persistence probability at a specific h 0 is also studied. Notably, all results obtained here are in agreement with those of the up-down symmetric models appeared in literatures despite the fact that the WV model is an asymmetric model. These results support the idea from other studies that the asymmetry in the WV is very weak.