Distribution of scaled height in one-dimensional competitive growth profiles

Abstract

This work investigates the scaled height distribution, ρ(q), of irregular profiles that are grown based on two sets of local rules: those of the restricted solid on solid (RSOS) and ballistic deposition (BD) models. At each time step, these rules are respectively chosen with probability p and r=1−p. Large-scale Monte Carlo simulations indicate that the system behaves differently in three succeeding intervals of values of p: IB≈[0,0.75),IT≈(0.75,0.9), and IR≈(0.9,1.0]. In IB, the ballistic character prevails: the growth velocity υ∞ decreases with p in a linear way, and similar behavior is found for Γ∞(p), the amplitude of the t1/3-fluctuations, which is measured from the second-order height cumulant. The distribution of scaled height fluctuations follows the Gaussian orthogonal ensemble (GOE) Tracy-Widom (TW) distribution with resolution roughly close to 10−4. The skewness and kurtosis of the computed distribution coincide with those for TW distribution. Similar results are observed in the interval IR, with prevalent RSOS features. In this case, the skewness become negative. In the transition interval IT, the system goes smoothly from one regime to the other: the height distribution becomes apparently Gaussian, which motivates us to identify this phenomenon as a transition from Kardar-Parisi-Zhang (KPZ) behavior to Edwards-Wilkinson (EW) behavior back to KPZ behavior.