Height distributions in competitive one-dimensional Kardar-Parisi-Zhang systems

TL;DR

This study investigates the height distribution and scaling behavior of a one-dimensional competitive RSOS-BD model, confirming asymptotic KPZ universality near a critical probability and analyzing crossover phenomena.

Contribution

It provides extensive numerical evidence that the model exhibits KPZ scaling and Tracy-Widom distributions near the critical point, clarifying crossover behaviors and improving previous findings.

Findings

System is asymptotically KPZ near p ≈ 0.83

Height distributions converge to GOE Tracy-Widom distribution

No Gaussian-GOE crossover observed in height distributions

Abstract

We study the competitive RSOS-BD model focusing on the validity of the Kardar-Parisi-Zhang (KPZ) ansatz h(t) = v t + (\Gamma t)^{\beta} \chi and the universality of the height distributions (HDs) near the point where the model has Edwards-Wilkinson (EW) scaling. Using numerical simulations for long times, we show that the system is asymptotically KPZ, as expected, for values of the probability of the RSOS component very close to p = p_c \approx 0.83. Namely, the growth exponents converge to \beta_{KPZ} = 1/3 and the HDs converge to the GOE Tracy-Widom distribution, however, the convergence seems to be faster in the last ones. While the EW-KPZ crossover appears in the roughness scaling in a broad range of probabilities p around p_c, a Gaussian-GOE crossover is not observed in the HDs into the same interval, possibly being restricted to values of p very close to p_c. These results improve recent ones reported by de Assis et al. [Phys. Rev. E 86, 051607 (2012)], where, based on smaller simulations, the KPZ scaling was argued to breakdown in broad range of p around p_c.