Anomalous roughening in competitive growth models with time-decreasing rates of correlated dynamics

TL;DR

This paper investigates how competitive lattice growth models with decreasing correlated dynamics rates exhibit anomalous roughening, establishing a scaling relation linking normal and anomalous exponents, supported by simulations and theoretical analysis.

Contribution

It extends the Family-Vicsek scaling relation to models with time-decreasing correlated growth rates, connecting anomalous and normal growth exponents.

Findings

Anomalous roughening occurs even with slow decay of correlated rates.

Scaling exponents can be derived from three anomalous exponents without detailed mechanism knowledge.

Simulation results support the extended scaling relation and observed anomalous effects.

Abstract

Lattice growth models where uncorrelated random deposition competes with some aggregation dynamics that generates correlations are studied with rates of the correlated component decreasing as a power law. These models have anomalous roughening, with anomalous exponents related to the normal exponents of the correlated dynamics, to an exponent characterizing the aggregation mechanism and to that power law exponent. This is shown by a scaling approach extending the Family-Vicsek relation previously derived for the models with time-independent rates, thus providing a connection of normal and anomalous growth models. Simulation results for several models support those conclusions. Remarkable anomalous effects are observed even for slowly decreasing rates of the correlated component, which may correspond to feasible temperature changes in systems with activated dynamics. The scaling exponents of the correlated component can be obtained only from the estimates of three anomalous exponents, without knowledge of the aggregation mechanism, and a possible application is discussed. For some models, the corresponding Edwards-Wilkinson and Kardar-Parisi-Zhang equations are also discussed.