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

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