Emergence in kinetic roughening with long-range temporal correlations

The role of long-range temporal correlations in kinetic roughening processes is significant, potentially influencing surface morphologies and dynamic scaling properties. This type of correlation, acting as a nonlocal interaction during growth processes, disrupts the self-affine fractal structure by causing the emergence of nontrivial global properties from individual local interactions. In this work, two typical discrete growth models, including random deposition and ballistic deposition, are investigated numerically in the presence of long-range temporal correlations. Two quantitative measurement methods, the Hellinger distance and the novelty detection, are used independently to determine whether emergence occurs. Our simulation results indicate that, above a critical threshold of temporal correlation exponent, the systems exhibit emergence behavior, consistent with the existence of nontrivial scaling properties and surface morphologies when long-range temporal correlations are presented.